centrality of trees for capacitated k k center we consider the capacitated k k center problem in this problem we are given a finite set of locations in a metric space and each location has an associated non negative integer capacity the goal is to choose open k k locations called centers and assign each location to an open center to minimize the maximum over all locations of the distance of the location to its assigned center the number of locations assigned to a center cannot exceed the center s capacity the uncapacitated k k center problem has a simple tight 2 2 approximation from the 80 s in contrast the first constant factor approximation for the capacitated problem was obtained only recently by cygan hajiaghayi and khuller who gave an intricate lp rounding algorithm that achieves an approximation guarantee in the hundreds in this paper we give a simple algorithm with a clean analysis and prove an approximation guarantee of 9 9 it uses the standard lp relaxation and comes close to settling the integrality gap after necessary preprocessing which is narrowed down to either 7 8 7 8 or 9 9 the algorithm proceeds by first reducing to special tree instances and then uses our best possible algorithm to solve such instances our concept of tree instances is versatile and applies to natural variants of the capacitated k k center problem for which we also obtain improved algorithms finally we give evidence to show that more powerful preprocessing could lead to better algorithms by giving an approximation algorithm that beats the integrality gap for instances where all non zero capacities are the same

improved approximation algorithms for the uncapacitated facility location problem we consider the uncapacitated facility location problem in this problem there is a set of locations at which facilities can be built a fixed cost fi is incurred if a facility is opened at location i furthermore there is a set of demand locations to be serviced by the opened facilities if the demand location j is assigned to a facility at location i then there is an associated service cost proportional to the distance between i and j cij the objective is to determine which facilities to open and an assignment of demand points to the opened facilities so as to minimize the total cost we assume that the distance function c is symmetric and satisfies the triangle inequality for this problem we obtain a 1 2 e approximation algorithm where 1 2 e approx 1 736 which is a significant improvement on the previously known approximation guarantees the algorithm works by rounding an optimal fractional solution to a linear programming relaxation our techniques use properties of optimal solutions to the linear program randomized rounding as well as a generalization of the decomposition techniques of shmoys tardos and aardal proceedings of the 29th acm symposium on theory of computing el paso tx 1997 pp 265 274

primal dual algorithms for deterministic inventory problems we consider several classical models in deterministic inventory theory the single item lot sizing problem the joint replenishment problem and the multistage assembly problem these inventory models have been studied extensively and play a fundamental role in broader planning issues such as the management of supply chains for each of these problems we wish to balance the cost of maintaining surplus inventory for future demand against the cost of replenishing inventory more frequently for example in the joint replenishment problem demand for several commodities is specified over a discrete finite planning horizon the cost of maintaining inventory is linear in the number of units held but the cost incurred for ordering a commodity is independent of the size of the order furthermore there is an additional fixed cost incurred each time a nonempty subset of commodities is ordered the goal is to find a policy that satisfies all demands on time and minimizes the overall holding and ordering cost we shall give a novel primal dual framework for designing algorithms for these models that significantly improve known results in several ways the performance guarantees for the quality of the solutions improve on or match previously known results the performance guarantees hold under much more general assumptions about the structure of the costs and the algorithms and their analysis are significantly simpler than previous known results finally our primal dual framework departs from the structure of previously studied primal dual approximation algorithms in significant ways and we believe that our approach may find applications in other settings more specifically we provide 2 approximation algorithms for the joint replenishment problem and for the assembly problem and solve the single item lot sizing problem to optimality the results for the joint replenishment and the lot sizing problems also hold for their generalizations with back orders allowed as a byproduct of our work we prove known and new upper bounds on the integrality gap of some linear programming lp relaxations of the abovementioned problems

heuristics for the fixed cost median problem we describe in this paper polynomial heuristics for three important hard problems the discrete fixed cost median problem the plant location problem the continuous fixed cost median problem in a euclidean space and the network fixed cost median problem with convex costs the heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points the derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem

a combinatorial primal dual approach to semidefinite programs semidefinite programs sdps have been used in many recent approximation algorithms we develop a general primal dual approach to solve sdps using a generalization of the well known multiplicative weights update rule to symmetric matrices for a number of problems such as s parsest c ut and b alanced s eparator in undirected and directed weighted graphs m in u n c ut and m in 2cnf d eletion this yields combinatorial approximation algorithms that are significantly more efficient than interior point methods the design of our primal dual algorithms is guided by a robust analysis of rounding algorithms used to obtain integer solutions from fractional ones our ideas have proved useful in quantum computing especially the recent result of jain et al 2011 that qip e pspace

on clusterings good bad and spectral we motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures a simple recursive heuristic is shown to have poly logarithmic worst case guarantees under the new measure the main result of the article is the analysis of a popular spectral algorithm one variant of spectral clustering turns out to have effective worst case guarantees another finds a good clustering if one exists

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

improved combinatorial algorithms for facility location problems we present improved combinatorial approximation algorithms for the uncapacitated facility location problem two central ideas in most of our results are cost scaling and greedy improvement we present a simple greedy local search algorithm which achieves an approximation ratio of 2 414 epsilon in tilde o n 2 epsilon time this also yields a bicriteria approximation tradeoff of 1 gamma 1 2 gamma for facility cost versus service cost which is better than previously known tradeoffs and close to the best possible combining greedy improvement and cost scaling with a recent primal dual algorithm for facility location due to jain and vazirani we get an approximation ratio of 1 853 in tilde o n 3 time this is very close to the approximation guarantee of the best known algorithm which is linear programming lp based further combined with the best known lp based algorithm for facility location we get a very slight improvement in the approximation factor for facility location achieving 1 728 we also consider a variant of the capacitated facility location problem and present improved approximation algorithms for this

primal dual approximation algorithm for the two level facility location problem via a dual quasi greedy approach the main contribution of this work is to propose a primal dual combinatorial 3 1 e approximation algorithm for the two level facility location problem 2 lflp by exploring the approximation oracle concept this result improves the previous primal dual 6 approximation algorithm for the multilevel facility location problem and also matches the previous primal dual approximation ratio for the single level facility location problem one of the major merits of primal dual type algorithms is their easy adaption to other variants of the facility location problems as a demonstration our primal dual approximation algorithm can be easily adapted to several variants of the 2 lflp including models with stochastic scenario dynamically arrived demands and linear facility cost

a family of level dependent biorthogonal wavelet filters for image compression abstract in this work we explore the construction and the applications of a special family of level dependent biorthogonal filters i e filters whose taps depend on the scaling level such a family is generated from a class of functions all related through level dependent or nonstationary refinement equations which contains cardinal polynomial b splines as a particular case the greater flexibility offered by the nonstationarity of these filters allows to achieve better results in some image processing problems such as image compression when compared to classical biorthogonal b spline filters

finding a collective set of items we consider the following problem there is a set of items e g movies and a group of agents e g passengers on a plane each agent has some intrinsic utility for each of the items our goal is to pick a set of k items that maximize the total derived utility of all the agents i e in our example we are to pick k movies that we put on the plane s entertainment system however the actual utility that an agent derives from a given item is only a fraction of its intrinsic one and this fraction depends on how the agent ranks the item among the chosen available ones we provide a formal specification of the model and provide concrete examples and settings where it is applicable we show that the problem is hard in general but we show a number of tractability results for its natural special cases

graph theory applied to noise and vibration control in statistical energy analysis models a fundamental aspect of noise and vibration control in statistical energy analysis sea models consists in first identifying and then reducing the energy flow paths between subsystems in this work it is proposed to make use of some results from graph theory to address both issues on the one hand linear and path algebras applied to adjacency matrices of sea graphs are used to determine the existence of any order paths between subsystems counting and labeling them finding extremal paths or determining the power flow contributions from groups of paths on the other hand a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one modifying as few internal and coupling loss factors as possible

complexity of the multicut problem in its vanilla partial and generalized versions in graphs of bounded treewidth abstract in the multicut problem the input consists of a graph and a set of pairs of terminal vertices that have to be disconnected by the removal of a set of edges with minimum total weight the partial multicut problem generalizes multicut by only requiring a given number of pairs of terminals to be disconnected by the removal of edges it has been shown that multicut remains apx hard if the treewidth t w g of its input graph g is bounded but that it is fpt w r t t w g h where h is the demand graph whose vertices are the terminals and whose edges are the pairs of terminals we prove that this also holds for partial multicut furthermore it has been proved that multicut also becomes polynomial time solvable if t w g is bounded and h is complete this is the multiterminal cut problem we extend this result in two directions by proving that multicut remains polynomial time solvable if t w g h is bounded and that this remains true for partial multicut finally we show that if we further generalize the problem to allow non unitary profits for pairs of terminals then the problem is weakly np hard and has an fptas if t w g h is bounded and becomes apx hard if t w g h is bounded

approximating k forest with resource augmentation a primal dual approach in this paper we study the k forest problem in the model of resource augmentation in the k forest problem given an edge weighted graph g v e a parameter k and a set of m demand pairs subseteq v times v the objective is to construct a minimum cost subgraph that connects at least k demands the problem is hard to approximate the best known approximation ratio is o min sqrt n sqrt k furthermore k forest is as hard to approximate as the notoriously hard densest k subgraph problem

incremental algorithms for facility location and k median in the incremental versions of facility location and k median the demand points arrive one at a time and the algorithm maintains a good solution by either adding each new demand to an existing cluster or placing it in a new singleton cluster the algorithm can also merge some of the existing clusters at any point in time for facility location we consider the case of uniform facility costs where the cost of opening a facility is the same for all points and present the first incremental algorithm which achieves a constant performance ratio using this algorithm as a building block we obtain the first incremental algorithm for k median which achieves a constant performance ratio using o k medians the algorithm is based on a novel merge rule which ensures that the algorithm s configuration monotonically converges to the optimal facility locations according to a certain notion of distance using this property we reduce the general case to the special case when the optimal solution consists of a single facility

lp based approximation algorithms for capacitated facility location in the capacitated facility location problem with hard capacities we are given a set of facilities mathcal f and a set of clients mathcal d in a common metric space each facility i has a facility opening cost f i and capacity u i that specifies the maximum number of clients that may be assigned to this facility we want to open some facilities from the set mathcal f and assign each client to an open facility so that at most u i clients are assigned to any open facility i the cost of assigning client j to facility i is given by the distance c ij and our goal is to minimize the sum of the facility opening costs and the client assignment costs the only known approximation algorithms that deliver solutions within a constant factor of optimal for this np hard problem are based on local search techniques it is an open problem to devise an approximation algorithm for this problem based on a linear programming lower bound or indeed to prove a constant integrality gap for any lp relaxation we make progress on this question by giving a 5 approximation algorithm for the special case in which all of the facility costs are equal by rounding the optimal solution to the standard lp relaxation one notable aspect of our algorithm is that it relies on partitioning the input into a collection of single demand capacitated facility location problems approximately solving them and then combining these solutions in a natural way

an improved 1 1 evolutionary algorithm for k median clustering problem with performance guarantee abstract evolutionary algorithms eas have been widely studied in numerical experiments and successfully applied in practice however most existing eas are designed without a theoretical analysis for their performance guarantee in this paper we define a fitness function to guide the well known 1 1 evolutionary algorithm called 1 1 ea to optimize the np hard k median problem we prove that the 1 1 ea can obtain a performance guarantee of 5 for k median problem in polynomial expected runtime o m n 2 d m a x if all distances between data points and cluster centers are integers where m and n are respectively the cardinalities of the data set and cluster center set and d m a x denotes the largest distance between data points and cluster centers to tackle the general case that the distances between data points and cluster centers are real number we propose an improved 1 1 ea which employs a distance scaling scheme during the evolutionary process our rigorous theoretical analysis shows that the improved 1 1 ea obtains a performance guarantee of 5 e in expected runtime o e 1 m n 2 log m d m a x where e 0 is a constant this study reveals that an appropriate scaling scheme can help eas to obtain a constant performance guarantee in polynomial expected runtime and provides insights into design eas for some np hard problems in addition we conduct experiment to compare the efficiency of the improved 1 1 ea with three clustering algorithms on optimizing three uci datasets

winner imposing strategyproof mechanisms for multiple facility location games we study facility location games where a number of facilities are placed in a metric space based on locations reported by strategic agents a mechanism maps the agents locations to a set of facilities the agents seek to minimize their connection cost namely the distance of their true location to the nearest facility and may even misreport their location we are interested in mechanisms that are strategyproof i e ensure that no agent can benefit from misreporting her location do not resort to monetary transfers and approximate the optimal social cost we focus on the closely related problems of k facility location and facility location with a uniform facility opening cost instead of a bound of k on the number of facilities in the former the social cost is the agents total connection cost while in the latter the social cost is the sum of the total connection cost and the total facility opening cost we mostly study mechanisms that are winner imposing in the sense that they allocate facilities to agents and require that each agent allocated a facility should connect to it we prove that the winner imposing version of the proportional mechanism proposed by lu et al 2010 18 is stategyproof for the k facility location game and achieves an approximation ratio of at most 4k for any k 1 for the facility location game we show that the winner imposing version of the randomized online algorithm of meyerson 2001 21 which has an approximation ratio of 8 is strategyproof furthermore we present a deterministic non imposing group strategyproof o logn approximate mechanism for the facility location game on the line we also consider oblivious winner imposing mechanisms for location games on continuous metric spaces and show that they are strategyproof iff they are locally strategyproof i e no agent can benefit by reporting a location arbitrarily close to her true location

approximation algorithms for constrained node weighted steiner tree problems we consider a class of optimization problems where the input is an undirected graph with two weight functions defined for each node namely the node s profit and its cost the goal is to find a connected set of nodes of low cost and high profit we present approximation algorithms for three natural optimization criteria that arise in this context all of which are np hard the budget problem asks for maximizing the profit of the set subject to a budget constraint on its cost the quota problem requires minimizing the cost of the set subject to a quota constraint on its profit finally the prize collecting problem calls for minimizing the cost of the set plus the profit here interpreted as a penalty of the complement set for all three problems our algorithms give an approximation guarantee of o log n where n is the number of nodes to the best of our knowledge these are the first approximation results for the quota problem and for the prize collecting problem both of which are at least as hard to approximate as the set cover for the budget problem our results improve on a previous o log 2 n result of guha et al our methods involve new theorems relating tree packings to node cut conditions we also show similar theorems with better bounds using edge cut conditions these imply bounds for the analogous budget and quota problems with edge costs which are comparable to known constant factor bounds

an approximation algorithm for the k median problem with uniform penalties via pseudo solution abstract we present a 1 3 approximation algorithm for the k median problem with uniform penalties extending the recent result by li and svensson for the classical k median problem without penalties one important difference of this work from that of li and svensson is a new definition of sparse instance to exploit the combinatorial structure of our problem

estimation of acoustic source strength by inverse methods part ii experimental investigation of methods for choosing regularization parameters two regularization methods tikhonov regularization and singular value discarding are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques in this paper some methods are investigated for choosing the tikhonov regularization parameter and the singular values to be discarded of these we concentrate on the use of ordinary cross validation and generalized cross validation these methods can provide an appropriate regularization parameter without prior knowledge of either the acoustic source strength or the contaminating measurement noise some experimental results obtained using a randomly vibrating simply supported plate mounted in a baffle are presented to illustrate the performance of the methods for choosing the regularization parameters

design of an optimal wave vector filter for enhancing the resolution of reconstructed source field by near field acoustical holography nah in near field acoustical holography using the boundary element method the reconstructed field often diverges due to the presence of small measurement errors in order to handle this instability in the inverse problem the reconstruction process should include some form of regularization for enhancing the resolution of source images the usual method of regularization has been the truncation of wave vectors associated with small singular values although the determination of an optimal truncation order is difficult in this article an iterative inverse solution technique is suggested in which the mean square error prediction is used a statistical estimation of the minimum mean square error between measured pressures and the model solution is required for yielding the optimal number of iterations the continuous curve of an optimal wave vector filter is designed for suppressing the high order modes that can produce large reconstruction errors experimental results from a baffled radiator reveal that the reconstruction errors can be reduced by this form of regularization by at least 48 compared to those without any regularization in comparison to results using the optimal truncation method of regularization the new scheme is shown to give further reductions of truncation error of between 7 and 39 for the example in this article

a faster better approximation algorithm for the minimum latency problem we give a 7 18 approximation algorithm for the minimum latency problem that uses only o n log n calls to the prize collecting steiner tree pcst subroutine of goemans and williamson this improves the previous best algorithms in both performance guarantee and running time a previous algorithm of goemans and kleinberg for the minimum latency problem requires an approximation algorithm for the k minimum spanning tree k mst problem which is called as a black box for each value of k their algorithm can achieve an approximation factor of 10 77 while making o n n log c log n pcst calls a factor of 8 98 using o n 3 n log c log n pcst calls or a factor of 7 18 epsilon using n o 1 epsilon log c pcst calls via the k mst algorithms of garg arya and ramesh and arora and karakostas respectively here n denotes the number of nodes in the instance and c is the largest edge cost in the input in all cases the running time is dominated by the pcst calls since the pcst subroutine can be implemented to run in o n 2 time the overall running time of our algorithm is o n 3 log n we also give a faster randomized version of our algorithm that achieves the same approximation guarantee in expectation but uses only o log 2 n pcst calls and derandomize it to obtain a deterministic algorithm with factor 7 18 epsilon using o frac 1 epsilon log 2 n pcst calls the basic idea for our improvement is that we do not treat the k mst algorithm as a black box this allows us to take advantage of some special situations in which the pcst subroutine delivers a 2 approximate k mst we are able to obtain the same approximation ratio that would be given by goemans and kleinberg if we had access to 2 approximate k msts for all values of k even though we have them only for some values of k that we are not able to specify in advance we also extend our algorithm to a weighted version of the minimum latency problem

dynamic force identification based on enhanced least squares and total least squares schemes in the frequency domain identifying dynamic forces from structural responses is necessary when direct measurement of those dynamic forces is impossible using conventional means a common approach to address this problem is to determine the frequency response function frf matrix measure the structural responses and calculate the dynamic forces based on least squares ls scheme this approach has been proven to be effective in reducing the random errors that occur in structural response signals unfortunately the accuracy of this approach is often hindered by the inversion of an ill conditioned frf matrix at frequencies near the structural resonances to overcome this inversion instability two regularization filters namely the truncated singular value decomposition tsvd filter and the tikhonov filter are used in conjunction with the conventional ls scheme at specific frequencies here a criterion for applying these enhanced ls schemes is proposed to aid in determining when the increase in computational effort is better utilized furthermore a new ls form of the morozov s discrepancy principle is formulated to aid in selecting the optimum regularization parameter for these filters at each frequency the accuracy in using conventional ls tsvd based ls and tikhonov filter based ls schemes are compared analytically and numerically in this paper it is found that for small sized frf matrices the tikhonov filter based ls scheme tends to work better than the tsvd filter based ls scheme since these approaches can only deal with the random errors in the measured structural responses a total least squares tls scheme that can also address errors associated with the frf matrix is proposed in this research numerical simulations demonstrate that under certain conditions the tls scheme is more effective in reducing the impact of these errors

a plant location guide for the unsure approximation algorithms for min max location problems this paper studies an extension of the k median problem under uncertain demand we are given an n vertex metric space v d and m client sets documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document s i subseteq v i 1 m end document the goal is to open a set of k facilities f such that the worst case connection cost over all the client sets is minimized i e documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document min f subseteq v f k max i in m left sum j in s i d

the ordered k median problem surrogate models and approximation algorithms in the last two decades a steady stream of research has been devoted to studying various computational aspects of the ordered k median problem which subsumes traditional facility location problems such as median center p centrum etc through a unified modeling approach given a finite metric space the objective is to locate k facilities in order to minimize the ordered median cost function in its general form this function penalizes the coverage distance of each vertex by a multiplicative weight depending on its ranking or percentile in the ordered list of all coverage distances while antecedent literature has focused on mathematical properties of ordered median functions integer programming methods various heuristics and special cases this problem was not studied thus far through the lens of approximation algorithms in particular even on simple network topologies such as trees or line graphs obtaining non trivial approximation guarantees is an open question the main contribution of this paper is to devise the first provably good approximation algorithms for the ordered k median problem we develop a novel approach that relies primarily on a surrogate model where the ordered median function is replaced by a simplified ranking invariant functional form via efficient enumeration surprisingly while this surrogate model is varomega n varomega 1 hard to approximate on general metrics we obtain an o log n approximation for our original problem by employing local search methods on a smooth variant of the surrogate function in addition an improved guarantee of 2 epsilon is obtained on tree metrics by optimally solving the surrogate model through dynamic programming finally we show that the latter optimality gap is tight up to an o epsilon term

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

convergence of nonstationary cascade algorithms a nonstationary multiresolution of l 2 mathbb r s is generated by a sequence of scaling functions phi k in l 2 mathbb r s k in mathbb z we consider phi k that is the solution of the nonstationary refinement equations phi k m sum j h k 1 j phi k 1 m cdot j k in mathbb z where h k is finitely supported for each k and m is a dilation matrix we study various forms of convergence in l 2 mathbb r s of the corresponding nonstationary cascade algorithm phi k n m sum j h k 1 j phi k 1 n 1 m cdot j as k or n tends to infty it is assumed that there is a stationary refinement equation at infty with filter sequence h and that sum k h k j h j infty the results show that the convergence of the nonstationary cascade algorithm is determined by the spectral properties of the transition operator associated with h

an improved method for the reconstruction of a distributed force acting on a vibrating structure indirectly reconstructing distributed forces from measured structural response is necessary when the direct measurement of these dynamic forces is not possible an improved method for reconstructing distributed forces is developed in this paper unlike the traditional modal method for force reconstruction the forcing spatial function is decomposed only over the known forcing region numerical simulations illustrate that when compared with the traditional modal method this new method tends to obtain better reconstruction results while requiring fewer basis functions a theoretical proof is provided to reveal the applicability and limitations of this new method it turns out that this approach like other inverse methods can also be an ill posed method to address this issue a regularization process is introduced to increase the inverse stability numerical results show that when the regularization process is applied to simulated response measurements that include noise the new method is able to reconstruct spatially distributed external forces with improved accuracy

effects of structural modes on vibratory force determination by the pseudoinverse technique the accuracy and effectiveness of the pseudoinverse technique as a means of determining the operating vibratory loads on a structural system from acceleration mobilities obtained by modal superposition can be severely undermined by lack of proper consideration of the participation of the structural modes at the frequency of interest methods of linear algebra and modal analysis are used to establish the limitations of this technique with regard to the number of independent forces determinable at a given frequency in relation to the number and significance of structural modes participating in the response at that frequency results of numerical calculations based on two uniform beams one cantilevered and the other free free show that for an assumed level of random error in the acceleration mobility matrix the accuracy of the determined forces correlates well with a parameter that is related to the number of modes contributing to the response of the structure at a given frequency

the checkpoint problem in this paper we consider the checkpoint problem the input consists of an undirected graph g a set of source destination pairs s 1 t 1 s 2 t 2 s k t k and a collection p of paths connecting the s i t i pairs a feasible solution is a multicut e namely a set of edges whose removal disconnects every source destination pair for each email protected p we define cp e p email protected e in the sum checkpoint scp problem the goal is to minimize p pcp e p while in the maximum checkpoint mcp problem the goal is to minimize max p pcp e p these problems have several natural applications e g in urban transportation and network security in a sense they combine the multicut problem and the minimum membership set cover problem for the sum objective we show that weighted scp is equivalent with respect to approximability to undirected multicut thus there exists an o logn approximation for scp in general graphs our current approximability results for the max objective have a wide gap we provide an approximation factor of o nlogn opt for mcp and a hardness of 2 under the assumption p np the hardness holds for trees this solves an open problem of nelson 2009 25 we complement the lower bound by an almost matching upper bound with an asymptotic approximation factor of 2 on trees with all s i t i having an ancestor descendant relation we give a combinatorial exact algorithm besides the algorithm being combinatorial its running time improves by many orders of magnitude the lp algorithm that follows from total unimodularity finally we show strong hardness for the well known problem of finding a path with minimum forbidden pairs which in a sense can be considered the dual to the checkpoint problem despite various works on this problem hardness of approximation was not known prior to this work we show that the problem cannot be approximated within cn for some constant c 0 unless p np this is the strongest type of hardness possible it carries over to directed acyclic graphs and is a huge improvement over the plain np hardness of gabow h n gabow finding paths and cycles of superpolylogarithmic length siam j comput 36 6 2007 1648 1671

a general approximation technique for constrained forest problems we present a general approximation technique for a large class of graph problems our technique mostly applies to problems of covering at minimum cost the vertices of a graph with trees cycles or paths satisfying certain requirements in particular many basic combinatorial optimization problems fit in this framework including the shortest path minimum cost spanning tree minimum weight perfect matching traveling salesman and steiner tree problems our technique produces approximation algorithms that run in o n 2 log n time and come within a factor of 2 of optimal for most of these problems for instance we obtain a 2 approximation algorithm for the minimum weight perfect matching problem under the triangle inequality our running time of o n 2 log n time compares favorably with the best strongly polynomial exact algorithms running in o n 3 time for dense graphs a similar result is obtained for the 2 matching problem and its variants we also derive the first approximation algorithms for many np complete problems including the non fixed point to point connection problem the exact path partitioning problem and complex location design problems moreover for the prize collecting traveling salesman or steiner tree problems we obtain 2 approximation algorithms therefore improving the previously best known performance guarantees of 2 5 and 3 respectively math programming 59 1993 pp 413 420

a combinatorial 2 375 approximation algorithm for the facility location problem with submodular penalties we offer the currently best approximation ratio 2 375 for the facility location problem with submodular penalties flpsp improving not only the previous best combinatorial ratio 3 but also the previous best non combinatorial ratio 2 488 we achieve this improved ratio by combining the primal dual scheme with the greedy augmentation technique

estimation of interfacial forces in time domain for linear systems abstract a structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces which are difficult to directly measure four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time invariant proportionally damped discrete systems first the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined next the frequency domain estimation methods based on the sub system concept are reviewed and an inverse fourier transform scheme is introduced an indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis the sub system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub system finally an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated although the proposed indirect methods are designed for eventual experimental applications this article provides numerical feasibility studies via a simple source path receiver system with parallel vibration paths that has five translational degrees of freedom the proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load without and with gaussian noise to observe the starting transients as well as subsequent motions and interfacial forces preliminary comparisons with a laboratory experiment are very promising

the primal dual method for approximation algorithms in this survey we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to np hard problems in combinatorial optimization because of parallels with the primal dual method commonly used in combinatorial optimization we call it the primal dual method for approximation algorithms we show how this technique can be used to derive approximation algorithms for a number of different problems including network design problems feedback vertex set problems and facility location problems

an efficient approximate algorithm for the 1 median problem in metric spaces we propose a simple and natural linear randomized algorithm for the approximate 1 median selection problem in metric spaces the 1 median of a finite subset s of a metric space is the element of s which minimizes the average distance from the remaining points in s this problem is extremely important in most applications using clustering of metric spaces but also in connection with several algorithms in bioinformatics the only linear approximation algorithm for the 1 median problem which provably works in any metric space without going through any euclidean space has been proposed by indyk in proceedings of the 31st annual acm symposium on theory of computing atlanta 1999 pp 428 432 however indyk s algorithm which is based on sufficiently large sampling turns out not to be a practical solution the same holds true even for its heuristic variants which use samplings of smaller size the algorithm we propose has a simple and efficient implementation which performs better than indyk s algorithm in practice on the other hand while the performance of indyk s algorithm is guaranteed by an approximation factor in the case of our algorithm we are only able to produce experimental evidence of its precision extensive experimentation has been performed on both synthetic and real input datasets synthetic datasets were generated with uniform and skewed distributions using various metrics real datasets have been extrapolated from real world official databases available on the web successful results of the proposed algorithm are reported for several applications in bioinformatics and various classes of approximate search queries

facility location with matroid or knapsack constraints in the classical k median problem we are given a metric space and want to open k centers so as to minimize the sum over all the vertices of the distance of each vertex to its nearest open center in this paper we present the first constant factor approximation algorithms for two natural generalizations of this problem that handle matroid or knapsack constraints in the matroid median problem there is an underlying matroid on the vertices and the set of open centers is constrained to be independent in this matroid when the matroid is uniform we recover the k median problem another previously studied special case is the red blue median problem where we have a partition matroid with two parts our algorithm for matroid median is based on rounding a natural linear programming relaxation in two stages and it relies on a connection to matroid intersection in the knapsack median problem centers have weights and the total weight of open centers is constrained to be at most a given capacity when all wei

comparison of methods for parameter selection in tikhonov regularization with application to inverse force determination in performing transfer path analysis of structure borne sound transmission the operational forces at the excitation points and or at the connections within the structure borne paths are required these forces can be obtained by using inverse techniques but the measured data used will contain some unknown errors therefore the reconstructed forces may include large errors due to the inversion of an ill conditioned matrix of these measured data in this study tikhonov regularization is used in order to improve the conditioning of the matrix inversion several methods are available to select the optimal regularization parameter the purpose of this paper is to compare the performance of the ordinary and generalized cross validation methods and the l curve criterion simulations are carried out representing measurements on a rectangular plate for different noise levels in measured data also the robustness of the conclusions is investigated by varying the shape of the plates the force positions and the noise levels included in the measured data the l curve method is found to perform better than ocv or gcv particularly for high noise levels in the operational responses but less well when these noise levels are low it is therefore found to be less susceptible to producing large reconstruction errors but it tends to over regularize the solution in the presence of low noise leading to under estimates of the forces in practice measurements of operational responses may be susceptible to noise contamination which suggests that the l curve method is likely to be the most appropriate method in practical situations nevertheless it is important to obtain good estimates of the likely noise in the signals before determining the most appropriate regularization technique ordinary cross validation method is generally found to have a better performance than generalized cross validation method if the matrix condition numbers are high since the need for regularization is greater with high condition numbers it is consequently found that the ordinary cross validation method gives more reliable results overall than the generalized cross validation method

clustering through continuous facility location problems we consider the continuous facility location problem conflp given a finite set of clients c r d and a number f r conflp consists in opening a set f r d of facilities each at cost f and connecting each client to an open facility the objective is to minimize the costs of opening facilities and connecting clients we reduce conflp to the standard facility location problem flp by using the so called approximate center sets this reduction preserves the approximation except for an error e and implies 1 488 e and 2 04 e approximations when the connection cost is given by the euclidean distance and the squared euclidean distance respectively moreover we obtain approximate center sets for the case that the connection cost is the th power of the euclidean distance achieving approximations for the corresponding problems for any 1 as a byproduct we also obtain a polynomial time approximation scheme for the k median problem with this cost function for any fixed k

structural source identification using a generalized tikhonov regularization abstract this paper addresses the problem of identifying mechanical exciting forces from vibration measurements the proposed approach is based on a generalized tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity to solve such a regularization problem efficiently a generalized iteratively reweighted least squares girls algorithm is introduced proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the girls algorithm

impact force sparse reconstruction from highly incomplete and inaccurate measurements abstract the classical l2 norm based regularization methods applied for force reconstruction inverse problem require that the number of measurements should not be less than the number of unknown sources taking into account the sparse nature of impact force in time domain we develop a general sparse methodology based on minimizing l1 norm for solving the highly underdetermined model of impact force reconstruction a monotonic two step iterative shrinkage thresholding mtwist algorithm is proposed to find the sparse solution to such an underdetermined model from highly incomplete and inaccurate measurements which can be problematic with tikhonov regularization mtwist is highly efficient for large scale ill posed problems since it mainly involves matrix vector multiplies without matrix factorization in sparsity frame the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact force simulation and experiment including single source and two source impact force reconstruction are conducted on a simply supported rectangular plate and a shell structure to illustrate the effectiveness and applicability of mtwist respectively both the locations and force time histories of the single source and two source cases are accurately reconstructed from a single accelerometer where the high noise level is considered in simulation and the primary noise in experiment is supposed to be colored noise meanwhile the consecutive impact forces reconstruction in a large scale greater than 104 sparse frame illustrates that mtwist has advantages of computational efficiency and identification accuracy over tikhonov regularization

a force identification method using cubic b spline scaling functions for force identification the solution may differ from the desired force seriously due to the unknown noise included in the measured data as well as the ill posedness of inverse problem in this paper an efficient basis function expansion method based on wavelet multi resolution analysis using cubic b spline scaling functions as basis functions is proposed for identifying force history with high accuracy which can overcome the deficiency of the ill posed problem the unknown force is approximated by a set of translated cubic b spline scaling functions at a certain level and thereby the original governing equation of force identification is reformulated to find the coefficients of scaling functions which yields a well posed problem the proposed method based on wavelet multi resolution analysis has inherent numerical regularization for inverse problem by changing the level of scaling functions the number of basis functions employed to approximate the identified force depends on the level of scaling functions a regularization method for selecting the optimal level of cubic b spline scaling functions by virtue of condition number of matrix is proposed in this paper the validity and applicability of the proposed method are illustrated by two typical examples of volterra fredholm integral equations that are both typical ill posed problems force identification experiments including impact and harmonic forces are conducted on a cantilever beam to compare the accuracy and efficiency of the proposed method with that of the truncated singular value decomposition tsvd technique

fuzzy identification of dynamic loads in presence of structural epistemic uncertainties abstract the interval identification of dynamic loads for uncertain structures was performed primarily by the interval perturbation method ipm influences of structural epistemic uncertainties on unknown loads cannot be effectively quantified for now and the interval inversion needs to be furtherly investigated in this paper tikhonov regularized technique for the inverse analysis is integrated into a non intrusive de re uncertainty procedure i e the dimension wise analysis to reconstruct unknown loads under structural epistemic uncertainties the proposed method transforms the interval identification model at zero cut of fuzzy inputs into a finite number of classical ones with crisp parameters regularized solutions to which are adopted to construct a polynomial approximation of each slice of the unknown load the extreme point set of each approximation at zero cut is derived to calculate its minimum maximum min max points at any alpha cut with respect to the corresponding uncertain parameter from which the min max input vectors of the unknown load are assembled in a dimension wise manner subsequently the interval bounds of the unknown load at each alpha cut can thus be evaluated by tikhonov regularized inversion based on which the fuzzy description is obtained the effectiveness of the proposed method is validated by the inclusion of the unknown load in the identified result and a tighter identified interval suggests its accuracy advantage over the ipm if the same regularization method is adopted

a tale of two methods we describe two widely used methods for the design and analysis of approximation algorithms the primal dual schema and the local ratio technique we focus on the creation of both methods by revisiting two results by bar yehuda and even the linear time primal dual approximation algorithm for set cover and its local ratio interpretation we also follow the evolution of the two methods by discussing more recent studies

multiresolution analyses originated from nonstationary subdivision schemes we analyze the properties of a new class of totally positive refinable functions obtained from nonstationary subdivision schemes we show that the corresponding system of the integer translates is linearly independent satisfies a whitney schoenberg condition reproduces polynomials up to a certain degree and generates a multiresolution analysis finally pre wavelets and bases on the interval are constructed

absolute and relative path measures in a discrete system by using two analytical methods this paper analytically examines two vibration paths rank ordering methods and critically investigates several path identification issues one method is the indirect interfacial path force estimation procedure that is employed in the well known experimental transfer path analysis the other method is path disconnect scheme that has been historically utilized in industry to empirically find a dominant or defective path in this article we utilize simplified but pedagogical discrete vibratory systems to clarify the underlying principles of both methods and to assess the path rank orders our analysis is limited to a linear time invariant system with only translating motions under harmonic excitation and three distinct parallel paths with or without masses are considered alternate formulations of the interfacial path forces based on direct and indirect methods are derived the indirect yet exact interfacial path force expressions could be used to estimate time averaged dissipated power and lagrangian energy spectra in various sub systems estimations using only the driving point frequency response functions are emphasized since they would ease the experimental burden next the path disconnect method is analytically formulated and related to the path connect scheme assuming one path at a time this analysis reveals some useful relations among the path measures and the way a particular path could be connected or disconnected a laboratory experiment validates the simplified massless path model which yields asymptotic trends finally all of the path rank orders are quantified and compared using many absolute and relative measures based on interfacial force receiver motion and sub system energy relationships direction for future work is briefly discussed

fpt approximation schemes for maximizing submodular functions we investigate the existence of approximation algorithms for maximization of submodular functions that run in a fixed parameter tractable fpt time given a non decreasing submodular set function v 2 x r v 2 x r the goal is to select a subset s of k elements from x such that v s v s is maximized we identify three properties of set functions referred to as p separability properties and we argue that many real life problems can be expressed as maximization of submodular p separable functions with low values of the parameter p we present fpt approximation schemes for the minimization and maximization variants of the problem for several parameters that depend on characteristics of the optimized set function such as p and k

a nearly linear time approximation scheme for the euclidean k median problem this paper provides a randomized approximation scheme for the k median problem when the input points lie in the d dimensional euclidean space the worst case running time is o 2 o log 1 epsilon varepsilon d 1 n log d 6 n which is nearly linear for any fixed varepsilon and d moreover our method provides the first polynomial time approximation scheme for and uncapacitated facility location instances in d dimensional euclidean space for any fixed d 2 our work extends techniques introduced originally by arora for the euclidean traveling salesman problem tsp to obtain the improvement we develop a structure theorem to describe hierarchical decomposition of solutions the theorem is based on an adaptive decomposition scheme which guesses at every level of the hierarchy the structure of the optimal solution and accordingly modifies the parameters of the decomposition we believe that our methodology is of independent interest and may find applications to further geometric problems

continuous speed scaling with variability a simple and direct approach abstract we consider an extension of the dynamic speed scaling scheduling model introduced by yao et al 1 a set of jobs each with a release time deadline and workload has to be scheduled on a single speed scalable processor both the maximum allowed speed of the processor and the energy costs may vary continuously over time the objective is to find a feasible schedule that minimizes the total energy costs theoretical algorithm design for speed scaling problems often tends to discretize problems as our tools in the discrete realm are often better developed or understood using the above speed scaling variant with variable continuous maximal processor speeds and energy prices as an example we demonstrate that a more direct approach via tools from variational calculus can not only lead to a very concise and elegant formulation and analysis but also avoids the explosion of variables constraints that often comes with discretizing 2 using well known tools from calculus of variations we derive combinatorial optimality characteristics for our continuous problem and provide a quite concise and simple correctness proof

approximation algorithms for data placement problems we develop approximation algorithms for the problem of placing replicated data in arbitrary networks where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data access cost we introduce the data placement problem to model this problem we have a set of caches mathcal f a set of clients mathcal d and a set of data objects mathcal o each cache i can store at most u i data objects each client j in mathcal d has demand d j for a specific data object o j in mathcal o and has to be assigned to a cache that stores that object storing an object o in cache i incurs a storage cost of f i o and assigning client j to cache i incurs an access cost of d jc ij the goal is to find a placement of the data objects to caches respecting the capacity constraints and an assignment of clients to caches so as to minimize the total storage and client access costs we present a 10 approximation algorithm for this problem our algorithm is based on rounding an optimal solution to a natural linear programming relaxation of the problem one of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant factor increase in the solution cost we also introduce the connected data placement problem to capture settings where write requests are also issued for data objects so that one requires a mechanism to maintain consistency of data we model this by requiring that all caches containing a given object be connected by a steiner tree to a root for that object which issues a multicast message upon a write to any copy of that object the total cost now includes the cost of these steiner trees we devise a 14 approximation algorithm for this problem we show that our algorithms can be adapted to handle two variants of the problem a a k median variant where there is a specified bound on the number of caches that may contain a given object and b a generalization where objects have lengths and the total length of the objects stored in any cache must not exceed its capacity

approximation algorithms for facility location problems with a special class of subadditive cost functions in this article we focus on approximation algorithms for facility location problems with subadditive costs as examples of such problems we present three facility location problems with stochastic demand and exponential servers respectively inventory we present a 1 e 1 reduction of the facility location problem with subadditive costs to the soft capacitated facility location problem which implies the existence of a 2 1 e approximation algorithm for a special subclass of subadditive functions we obtain a 2 approximation algorithm by reduction to the linear cost facility location problem

the quantification of structure borne transmission paths by inverse methods part 1 improved singular value rejection methods structure borne sound from installed machinery is often transmitted into a receiver structure via many connection points and several co ordinate directions at each of them in order to quantify the contributions from the various connection points the operational forces at the interfaces or an equivalent set of forces at some other locations should be determined these forces may be combined with measured transfer functions to determine their contributions to the sound at the receiver locations inverse methods are becoming widely used in which a matrix of measured accelerances is inverted at each frequency and used with operational acceleration data to find the forces due to poor conditioning of this matrix however the results can often be unreliable in this paper using both simulations and measurements an assessment is made of the success and failure of various strategies for dealing with the problems of ill conditioning in particular over determination and singular value rejection in each case the test structure is a rectangular plate and a wide frequency range is covered to include regions of both low and high modal overlap critical for the rejection of singular values is a suitable threshold it is established that previously used thresholds based on estimates of error in either accelerances or operational responses cannot be used universally an alternative approach is developed in which the accelerance matrix is perturbed by a different amount for each sample of the operational responses based on this approach a more robust strategy is proposed which takes account simultaneously of the effect of errors in both the accelerances and operational responses

a load identification method based on wavelet multi resolution analysis abstract load identification as a kind of indirect identification method uses system characteristic and responses to calculate loads a method based on wavelet multi resolution analysis is proposed in this paper by wavelet decomposition and transform at certain resolutions the proposed method transforms the convolution relation between responses and loads in time domain into the linear multiplicative relation between system responses and wavelet responses in the wavelet domain loads can be identified as long as the linear multiplicative relation is solved qualitative and quantitative rules are proposed for selecting parameters that affect the accuracy of the proposed method and are illustrated via numerical investigations the method is illustrated by a multi input multi output numerical simulation a multi input multi output laboratory experiment is performed to compare the proposed method with the frequency method on the identification ability

a constant approximation algorithm for the one warehouse multiretailer problem deterministic inventory theory provides streamlined optimization models that attempt to capture trade offs in managing the flow of goods through a supply chain we will consider two well studied deterministic inventory models called the one warehouse multiretailer owmr problem and its special case the joint replenishment problem jrp and give approximation algorithms with worst case performance guarantees that is for each instance of the problem our algorithm produces a solution with cost that is guaranteed to be at most 1 8 times the optimal cost this is called a 1 8 approximation algorithm our results are based on an lp rounding approach we provide the first constant approximation algorithm for the owmr problem and improve the previous results for the jrp

clustering under approximation stability a common approach to clustering data is to view data objects as points in a metric space and then to optimize a natural distance based objective such as the k median k means or min sum score for applications such as clustering proteins by function or clustering images by subject the implicit hope in taking this approach is that the optimal solution for the chosen objective will closely match the desired target clustering e g a correct clustering of proteins by function or of images by who is in them however most distance based objectives including those mentioned here are np hard to optimize so this assumption by itself is not sufficient assuming p np to achieve clusterings of low error via polynomial time algorithms in this article we show that we can bypass this barrier if we slightly extend this assumption to ask that for some small constant c not only the optimal solution but also all c approximations to the optimal solution differ from the target on at most some e fraction of points we call this c e approximation stability we show that under this condition it is possible to efficiently obtain low error clusterings even if the property holds only for values c for which the objective is known to be np hard to approximate specifically for any constant c 1 c e approximation stability of k median or k means objectives can be used to efficiently produce a clustering of error o e with respect to the target clustering as can stability of the min sum objective if the target clusters are sufficiently large thus we can perform nearly as well in terms of agreement with the target clustering as if we could approximate these objectives to this np hard value

approximation algorithms for the set covering and vertex cover problems we propose a heuristic that delivers in o n 3 steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

shape preserving c1 hermite interpolants generated by a gori pitolli subdivision scheme in this paper we present a method for the construction of c 1 hermite interpolants obtained from a particular family of refinable spline functions introduced by gori and pitolli they constitute a one parameter subfamily of the hermite interpolants generated by the general merrien s subdivision scheme we compare this family to the other one parameter subfamily studied by merrien and sablonniere and lyche and merrien on the solution of two points hermite interpolation problems with arbitrary monotonicity or convexity constraints

a simple and deterministic competitive algorithm for online facility location this paper presents a deterministic and efficient algorithm for online facility location the algorithm is based on a simple hierarchical partitioning and is extremely simple to implement it also applies to a variety of models i e models where the facilities can be placed anywhere in the region or only at customer sites or only at fixed locations the paper shows that the algorithm is o log n competitive under these various models where n is the total number of customers it also shows that the algorithm is o 1 competitive with high probability and for any arrival order when customers are uniformly distributed or when they follow a distribution satisfying a smoothness property experimental results for a variety of scenarios indicate that the algorithm behaves extremely well in practice

partial multicuts in trees let t v e be an undirected tree in which each edge is associated with a non negative cost and let s1 t1 sk tk be a collection of k distinct pairs of vertices given a requirement parameter t k the partial multicut on a tree problem asks to find a minimum cost set of edges whose removal from t disconnects at least t out of these k pairs this problem generalizes the well known multicut on a tree problem in which we are required to disconnect all given pairs the main contribution of this paper is an 8 3 e approximation algorithm for partial multicut on a tree whose run time is strongly polynomial for any fixed e 0 this result is achieved by introducing problem specific insight to the general framework of using the lagrangian relaxation technique in approximation algorithms our algorithm utilizes a heuristic for the closely related prize collecting variant in which we are not required to disconnect all pairs but rather incur penalties for failing to do so we provide a lagrangian multiplier preserving algorithm for the latter problem with an approximation factor of 2 finally we present a new 2 approximation algorithm for multicut on a tree based on lp rounding

the complexity of multiterminal cuts in the multiterminal cut problem one is given an edge weighted graph and a subset of the vertices called terminals and is asked for a minimum weight set of edges that separates each terminal from all the others when the number k of terminals is two this is simply the mincut max flow problem and can be solved in polynomial time it is shown that the problem becomes np hard as soon as k 3 but can be solved in polynomial time for planar graphs for any fixed k the planar problem is np hard however if k is not fixed a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 2 k of the optimal cut weight is also described

a systematic approach to bound factor revealing lps and its application to the metric and squared metric facility location problems a systematic technique to bound factor revealing linear programs is presented we show how to derive a family of upper bound factor revealing programs upfrp and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm obtaining an upfrp is straightforward and can be used as an alternative to analytical proofs that are usually very long and tedious we apply this technique to the metric facility location problem mflp and to a generalization where the distance function is a squared metric we call this generalization the squared metric facility location problem smflp and prove that there is no approximation factor better than 2 04 2 04 assuming mathrm p ne mathrm np p np then we analyze the best known algorithms for the mflp based on primal dual and lp rounding techniques when they are applied to the smflp we prove very tight bounds for these algorithms and show that the lp rounding algorithm achieves a ratio of 2 04 2 04 and therefore has the best possible factor for the smflp we use upfrps in the dual fitting analysis of the primal dual algorithms for both the smflp and the mflp improving some of the previous analysis for the mflp

total positivity and its applications preface i spline functions total positivity of the spline kernel and its applications b bojanov total positivity properties of lb splines t lyche l l schumaker total positivity and splines k morken totally positive systems and interpolation by subspaces of generalized splines m sommer h strauss ii matrix theory preservation of total nonnegativity under the hadamard product and related topics j garloff d g wagner vertex implications for totally nonnegative under the hadamard product and related topics j garloff on factorizations of totally positive matrices j garloff on factorizations of totally positive matrices m gasca j m pena iii geometric modeling total positivity and optimal bases j m carnicer j m pena total positivity and the shape of curves t n t goodman tchebycheff curves m l mazure h pottmann iv probability and mathematical biology analytical and probabilistic methods for totally positive matrices g s goodman some inequalities of total positivity in pure and applied mathematics s karlin z ziegler new directions and problems of multivariate total positivity motivated by genetic recombination probabilities s karlin v approximation theory tchebycheff spaces and total positivity j m carnicer j m pena cebysev and weak cebysev systems r a zalik vi complex analysis zero sets of entire fourier transforms of multiply positive density functions o m katkova vii statistics total nonnegativity of moment matrices and its application to e optimal designs in polynomial regression b heiligers analysis of regression dependence in 2 xn bivariate distributions and some applications in contingency tables s kasala m b rao viii real analysis total positivity and nonlinear analysis r q jia solutions of certain functional equations s karlin alternance and snakes in the nonlinear finite moment problem k tatalian ix combinatorics the applications of total positivity to combinatorics and conversely f brenti x integral equations spectral properties of totally positive kernels and matrices a pinkus index

approximate max flow min multi cut theorems and their applications consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed we prove the following approximate max flow min multicut theorem dst frac mbox rm min multicut o log k leq mbox rm max flow leq mbox rm min multicut noindent where k is the number of commodities our proof is constructive it enables us to find a multicut within o log k of the max flow and hence also the optimal multicut in addition the proof technique provides a unified framework in which one can also analyse the case of flows with specified demands of leighton and rao and klein et al and thereby obtain an improved bound for the latter problem

sparse regularization for force identification using dictionaries abstract the classical function expansion method based on minimizing l 2 norm of the response residual employs various basis functions to represent the unknown force its difficulty lies in determining the optimum number of basis functions considering the sparsity of force in the time domain or in other basis space we develop a general sparse regularization method based on minimizing l 1 norm of the coefficient vector of basis functions the number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process first according to the profile of the unknown force the dictionary composed of basis functions is determined second a sparsity convex optimization model for force identification is constructed third given the transfer function and the operational response sparse reconstruction by separable approximation sparsa is developed to solve the sparse regularization problem of force identification finally experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of sparsa besides the dirac dictionary other three sparse dictionaries including db6 wavelets sym4 wavelets and cubic b spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame the discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal square and triangular forces conversely the traditional tikhonov regularization method with the l curve criterion fails to identify both the impact and harmonic forces in these cases

approximate k msts and k steiner trees via the primal dual method and lagrangean relaxation garg 10 gives two approximation algorithms for the minimum cost tree spanning k vertices in an undirected graph recently jain and vazirani 15 discovered primal dual approximation algorithms for the metric uncapacitated facility location and k median problems in this paper we show how garg s algorithms can be explained simply with ideas introduced by jain and vazirani in particular via a lagrangean relaxation technique together with the primal dual method for approximation algorithms we also derive a constant factor approximation algorithm for the k steiner tree problem using these ideas and point out the common features of these problems that allow them to be solved with similar techniques

approximation algorithms for metric facility location and k median problems using the primal dual schema and lagrangian relaxation we present approximation algorithms for the metric uncapacitated facility location problem and the metric k median problem achieving guarantees of 3 and 6 respectively the distinguishing feature of our algorithms is their low running time o m log m and o m log m l log n respectively where n and m are the total number of vertices and edges in the underlying complete bipartite graph on cities and facilities the main algorithmic ideas are a new extension of the primal dual schema and the use of lagrangian relaxation to derive approximation algorithms

an approximation algorithm for the k prize collecting multicut on a tree problem abstract in this paper we consider the k prize collecting multicut on a tree k pcm t problem in this problem we are given an undirected tree t v e a set of m distinct pairs of vertices p s 1 t 1 s m t m and a parameter k with k m every edge in e has a nonnegative cost c e every pair s i t i in p has a nonnegative penalty cost i our goal is to find a multicut m that separates at least k pairs in p such that the total cost including the edge cost of the multicut m and the penalty cost of the pairs not separated by m is minimized this problem generalizes the well known multicut on a tree problem our main work is to present a 4 e approximation algorithm for the k pcm t problem via the methods of primal dual and lagrangean relaxation where e is any fixed positive number

experimental study of the mapping relationship based near field acoustic holography with spherical fundamental solutions abstract this paper is a consequent work of the previously proposed mapping relationship based near field acoustic holography mrs based nah h j wu w k jiang and h b zhang jsv 373 66 88 2016 it is devoted to the performance study of its practical application with error analysis and experimental validation two types of errors the truncation errors due to the limited number of participant modes and the inevitable measurement errors caused by uncertainties in the experiment are considered in the analysis the influences of the errors on the performance of mrs based nah are systematically investigated first of all expression of the relative reconstruction error of the pressure energy is derived based on the two types of errors an approach is developed to estimate the lower and upper bounds of the relative error it gives a guide to predict the error for a reconstruction under the condition that the truncation error and the signal to noise ratio are given then the condition number of the inverse operator is investigated to measure the sensitivity of the reconstruction to the input errors asymptotic expressions of the condition number for a special case conformal spherical model and hologram are obtained which indicates the condition number has a geometric growth with the number of participant modes numerical examples with different kinds of errors are elaborately designed to validate the stability as well as the correctness of the error analysis at last the mrs based nah is further examined and verified by a physical experiment a vibrating cubic model reconstructed from measurement on a spherical hologram a satisfied agreement with the directly measured pressure on a validation surface is observed for both quantity and distribution of the reconstructed pressure

on the parameterized complexity of separating certain sources from the target abstract multicut is proven to be fpt parameterized by the size of the cutset p we focus on its generalization partial multicut setting the number of pairs of terminals to be separated as a parameter r it asks for the minimum edge vertex cut whose removal would separate r sources s i from their target t i our main contributions concern its single target subproblem partial one target cut potc we show that potc when edges are to be cut is fpt parameterized by the cutset size p but is w 1 hard when parameterized only with r the vertex cutting version of potc is w 1 hard regardless of parameter configurations involving r and p

totally positive functions through nonstationary subdivision schemes in this paper a new class of nonstationary subdivision schemes is proposed to construct functions having all the main properties of b splines namely compact support central symmetry and total positivity we show that the constructed nonstationary subdivision schemes are asympotically equivalent to the stationary subdivision scheme associated with a b spline of suitable degree but the resulting limit function has smaller support than the b spline although keeping its regularity

a general framework of hierarchical clustering and its applications hierarchical clustering problem is a traditional topic in computer science which aims to discover a consistent hierarchy of clusters with different granularities one of the most important open questions on hierarchical clustering is the identification of the meaningful clustering levels in the hierarchical structure in this paper we answer this question from algorithmic point of view in particular we derive a quantitative analysis on the impact of the low level clustering costs on high level clusters when agglomerative algorithms are run to construct the hierarchy this analysis enables us to find meaningful clustering levels which are independent of the clusters hierarchically beneath it we thus propose a general agglomerative hierarchical clustering framework which automatically constructs meaningful clustering levels this framework is proven to be generally applicable to any k clustering problem in any relaxed metric space in which strict triangle inequality is relaxed within some constant factor to fully utilize the hierarchical clustering framework we conduct some case studies on k median and k means clustering problems in both of which our framework achieves better approximation factor than the state of the art methods we also extend our framework to handle the data stream clustering problem which allows only one scan on the whole data set by incorporating our framework into guha s data stream clustering algorithm the clustering quality is greatly enhanced with only small extra computation cost incurred the extensive experiments show that our proposal is superior to the distance based agglomerative hierarchical clustering and data stream clustering algorithms on a variety of data sets

integrality gaps for strengthened linear relaxations of capacitated facility location metric uncapacitated facility location is a well studied problem for which linear programming methods have been used with great success in deriving approximation algorithms capacitated facility location cfl is a generalization for which there are local search based constant factor approximations while there is no known compact relaxation with constant integrality gap this paper produces through a host of impossibility results the first comprehensive investigation of the effectiveness of mathematical programming for metric capacitated facility location with emphasis on lift and project methods we show that the relaxations obtained from the natural lp at varomega n n levels of the semidefinite lovasz schrijver hierarchy for mixed programs and at varomega n n levels of the sherali adams hierarchy have an integrality gap of varomega n n where n n is the number of facilities partially answering an open question of an et al centrality of trees for capacitated k center 2013 li and svensson proceedings of 45th acm symposium on theory of computing stoc 13 acm pp 901 910 2013 for the families of instances we consider both hierarchies yield at the n nth level an exact formulation for cfl thus our bounds are asymptotically tight building on our methodology for the sherali adams result we prove that the standard cfl relaxation enriched with the submodular inequalities of aardal et al math oper res 20 562 582 1995 a generalization of the flow cover valid inequalities has also an varomega n n gap and thus not bounded by any constant this disproves a long standing conjecture of levi et al math program 131 1 2 365 379 2012 we finally introduce the family of proper relaxations which generalizes to its logical extreme the classic star relaxation and captures general configuration style lps we characterize the behavior of proper relaxations for cfl through a sharp threshold phenomenon

improved algorithms for joint optimization of facility locations and network connections abstract this paper studies a k median steiner forest problem that jointly optimizes the opening of at most k facility locations and their connections to the client locations so that each client is connected by a path to an open facility with the total connection cost minimized the problem has wide applications in the telecommunication and transportation industries but is strongly np hard in the literature only a 2 approximation algorithm is known it being based on a lagrangian relaxation of the problem and using a sophisticated primal dual schema in this study we have developed an improved approximation algorithm using a simple transformation from an optimal solution of a minimum spanning tree problem compared with the existing 2 approximation algorithm our new algorithm not only achieves a better approximation ratio that is easier to be proved but also guarantees to produce solutions of equal or better quality up to 50 percent improvement in some cases in addition for two non trivial special cases where either every location contains a client or all the locations are in a tree shaped network we have developed for the first time in the literature new algorithms that can solve the problem to optimality in polynomial time

when trees collide an approximation algorithm for thegeneralized steiner problem on networks we give the first approximation algorithm for the generalized network steiner problem a problem in network design an instance consists of a network with link costs and for each pair i j of nodes an edge connectivity requirement r ij the goal is to find a minimum cost network using the available links and satisfying the requirements our algorithm outputs a solution whose cost is within 2 lceil log 2 r 1 rceil of optimal where r is the highest requirement value in the course of proving the performance guarantee we prove a combinatorial min max approximate equality relating minimum cost networks to maximum packings of certain kinds of cuts as a consequence of the proof of this theorem we obtain an approximation algorithm for optimally packing these cuts we show that this algorithm has application to estimating the reliability of a probabilistic network

monotone covering problems with an additional covering constraint we provide preliminary results regarding the existence of a polynomial time approximation scheme ptas for minimizing a linear function over a 0 1 covering polytope which is integral with one additional covering constraint our algorithm is based on extending the methods of goemans and ravi for the constrained minimum spanning tree problem and in particular implies the existence of a ptas for several covering integer programming problems with a totally unimodular constraint matrix these include the cases when the columns of the constraint matrix either have at most two nonzero elements are incidence vectors of a laminar family or have consecutive ones and no column is contained in another

the quantification of structure borne transmission paths by inverse methods part 2 use of regularization techniques the inversion of an ill conditioned matrix of measured data lies at the heart of procedures for the quantification of structure borne sources and transmission paths in an earlier paper the use of over determination singular value decomposition and the rejection of small singular values was discussed in the present paper alternative techniques for regularizing the matrix inversion are considered such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography the application to structure borne sound transmission involves matrices which vary much more with frequency and from one element to another in this study tikhonov regularization is used with the ordinary cross validation method for selecting the regularization parameter an iterative inversion technique is also studied here a form of cross validation is developed allowing an optimum value of the iteration parameter to be selected simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques experiments are also performed to validate the results both techniques are found to give considerably improved results compared to singular value rejection