minimum fill in inapproximability and almost tight lower bounds abstract given an n n sparse symmetric matrix with m nonzero entries performing gaussian elimination may turn some zeroes into nonzero values so called fill ins the minimum fill in problem asks whether it is possible to perform the elimination with at most k fill ins we exclude the existence of polynomial time approximation schemes for this problem assuming p np and the existence of 2 o n 1 time approximation schemes for any positive assuming the exponential time hypothesis we also give a 2 o k 1 2 n o 1 parameterized lower bound all these results come as corollaries of a new reduction from vertex cover to the minimum fill in problem which might be of its own interest all previous reductions for similar problems start from some kind of graph layout problems and hence have limited use in understanding their fine grained complexity

adjustable robust solutions of uncertain linear programs we consider linear programs with uncertain parameters lying in some prescribed uncertainty set where part of the variables must be determined before the realization of the uncertain parameters non adjustable variables while the other part are variables that can be chosen after the realization adjustable variables we extend the robust optimization methodology 1 3 6 9 13 14 to this situation by introducing the adjustable robust counterpart arc associated with an lp of the above structure often the arc is significantly less conservative than the usual robust counterpart rc however in most cases the arc is computationally intractable np hard this difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data the ensuing affinely adjustable robust counterpart aarc problem is then shown to be in certain important cases equivalent to a tractable optimization problem typically an lp or a semidefinite problem and in other cases having a tight approximation which is tractable the aarc approach is illustrated by applying it to a multi stage inventory management problem

parameterized and approximation complexity of partial vc dimension abstract we introduce the problem partial vc dimension that asks given a hypergraph h x e and integers k and l whether one can select a set c x of k vertices of h such that the set e c e e of distinct hyperedge intersections with c has size at least l the sets e c define equivalence classes over e partial vc dimension is a generalization of vc dimension which corresponds to the case l 2 k and of distinguishing transversal which corresponds to the case l e the latter is also known as test cover in the dual hypergraph we also introduce the associated fixed cardinality maximization problem max partial vc dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices we study the algorithmic complexity of partial vc dimension and max partial vc dimension both on general hypergraphs and on more restricted instances in particular neighborhood hypergraphs of graphs

a comparison of finite element based inversion algorithms local frequency estimation and direct inversion approach used in mre in quantitative elastography maps of the mechanical properties of soft tissue or elastograms are calculated from the measured displacement data by solving an inverse problem the model assumptions have a significant effect on elastograms motivated by the high sensitivity of imaging results to the model assumptions for in vivo magnetic resonance elastography of the prostate we compared elastograms obtained with four different methods two finite element method fem based methods developed by our group were compared with two other commonly used methods local frequency estimator lfe and curl based direct inversion c di all the methods assume a linear isotropic elastic model but the methods vary in their assumptions such as local homogeneity or incompressibility and in the specific approach used we report results using simulations phantom and ex vivo and in vivo data the simulation and phantom studies show for regions with an inclusion that the contrast to noise ratio cnr for the fem methods is about three to five times higher than the cnr for the lfe and c di and the rms error is about half the lfe method produces very smooth results i e low cnr and is fast c di is faster than the fem methods but it is only accurate in areas where elasticity variations are small the artifacts resulting from the homogeneity assumption in c di is detrimental in regions with large variations the ex vivo and in vivo results also show similar trends as the simulation and phantom studies the c fem method is more sensitive to noise compared with the mixed fem due to higher orders derivatives this is especially evident at lower frequencies where the wave curvature is smaller and it is more prone to such error causing a discrepancy in the absolute values between the mixed fem and c fem in our in vivo results in general the proposed fems use fewer simplifying assumptions and outperform the other methods but they are computationally more expensive

feature adaptive motion tracking of ultrasound image sequences using a deformable mesh by exploiting the correlation of ultrasound speckle patterns that result from scattering by underlying tissue elements two dimensional tissue motion theoretically can be recovered by tracking the apparent movement of the associated speckle patterns speckle tracking however is an ill posed inverse problem because of temporal decorrelation of the speckle patterns and the inherent low signal to noise ratio of medical ultrasonic images this paper investigates the use of an adaptive deformable mesh for nonrigid tissue motion recovery from ultrasound images the nodes connecting the mesh elements are allocated adaptively to stable speckle patterns that are less susceptible to temporal decorrelation the authors use the approach of finite clement analysis in manipulating the irregular mesh elements a novel deformable block matching algorithm making use of a lagrange element for higher order description of local motion is proposed to estimate a nonrigid motion vector at each node in order to ensure that the motion estimates are admissible to a physically plausible solution the nodal displacements are regularized by minimizing the strain energy associated with the mesh deformations experiments based on ultrasound images of a tissue mimicking phantom and a muscle undergoing contraction and on computer simulations have shown that the proposed algorithm can successfully track nonrigid displacement fields

excluded grid minors and efficient polynomial time approximation schemes two of the most widely used approaches to obtain polynomial time approximation schemes ptass on planar graphs are the lipton tarjan separator based approach and baker s approach in 2005 demaine and hajiaghayi strengthened both approaches using bidimensionality and obtained efficient polynomial time approximation schemes eptass for several problems including c onnected d ominating s et and f eedback v ertex s et in this work we unify the two strengthened approaches to combine the best of both worlds we develop a framework allowing the design of eptas on classes of graphs with the subquadratic grid minor sqgm property roughly speaking a class of graphs has the sqgm property if for every graph g from the class the fact that g contains no t t grid as a minor guarantees that the treewidth of g is subquadratic in t for example the class of planar graphs and more generally classes of graphs excluding some fixed graph as a minor have the sqgm property at the heart of our framework is a decomposition lemma stating that for most bidimensional problems on a graph class g with the sqgm property there is a polynomial time algorithm that given a graph g e g as input and an e 0 outputs a vertex set x of size e opt such that the treewidth of g x is f e here opt is the objective function value of the problem in question and f is a function depending only on e this allows us to obtain eptass on apex minor free graphs for all problems covered by the previous framework as well as for a wide range of packing problems partial covering problems and problems that are neither closed under taking minors nor contractions to the best of our knowledge for many of these problems including c ycle p acking f p acking f d eletion m ax l eaf s panning t ree or p artial r d ominating s et no eptass even on planar graphs were previously known we also prove novel excluded grid theorems in unit disk and map graphs without large cliques using these theorems we show that these classes of graphs have the sqgm property based on the developed framework we design eptass and subexponential time parameterized algorithms for various classes of problems on unit disk and map graphs

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

specializations and generalizations of the stackelberg minimum spanning tree game let be given a graph g v e whose edge set is partitioned into a set r of red edges and a set b of blue edges and assume that red edges are weighted and form a spanning tree of g then the stackelberg minimum spanning tree stackmst problem is that of pricing i e weighting the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized stackmst is known to be apx hard already when the number of distinct red edge weights is 2 in this paper we analyze some meaningful specializations and generalizations of stackmst which shed some more light on the computational complexity of the problem more precisely we first show that if g is restricted to be complete then the following holds i if there are only 2 distinct red edge weights then the problem can be solved optimally this contrasts with the corresponding apx hardness of the general problem ii otherwise the problem can be approximated within 7 4 for any 0 afterwards we define a natural extension of stackmst namely that in which blue edges are associated with a non negative activation cost and it is given a global activation budget that can be used and must not be exceeded in order to activate a subset of blue edges to be priced here after showing that the very same approximation ratio as that of the original problem can be achieved we prove that if the spanning tree of red edges can be rooted so as that any root leaf path contains at most h edges then the problem admits a 2 h approximation algorithm for any 0

inapproximability of maximal strip recovery in comparative genomics the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes for the reliable recovery of syntenic blocks noise and ambiguities in the genomic maps need to be removed first maximal strip recovery msr is an optimization problem proposed by zheng zhu and sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities given d genomic maps as sequences of gene markers the objective of msr d is to find d subsequences one subsequence of each genomic map such that the total length of syntenic blocks in these subsequences is maximized for any constant d 2 a polynomial time 2d approximation for msr d was previously known in this paper we show that for any d 2 msr d is apx hard even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map moreover we provide the first explicit lower bounds on approximating msr d for all d 2 in particular we show that msr d is np hard to approximate within w d logd from the other direction we show that the previous 2d approximation for msr d can be optimized into a polynomial time algorithm even if d is not a constant but is part of the input we then extend our inapproximability results to several related problems including cmsr d d gap msr d and d gap cmsr d

on the complexity of the vector connectivity problem we study a relaxation of the vector domination problem called vector connectivity veccon given a graph g with a requirement r v for each vertex v veccon asks for a minimum cardinality set s of vertices such that every vertex v v s is connected to s via r v disjoint paths in the paper introducing the problem boros et al 4 gave polynomial time solutions for veccon in trees cographs and split graphs and showed that the problem can be approximated in polynomial time on n vertex graphs to within a factor of log n 2 leaving open the question of whether the problem is np hard on general graphs we show that veccon is apx hard in general graphs and np hard in planar bipartite graphs and in planar line graphs we also generalize the polynomial result for trees by solving the problem for block graphs

deriving robust counterparts of nonlinear uncertain inequalities in this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters we use convex analysis support functions conjugate functions fenchel duality and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints it turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function conveniently these two computations are completely independent this approach has several advantages first it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities second it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived we also study some cases where the inequality is nonconcave in the uncertain parameters

on the approximability of single machine scheduling with precedence constraints we consider the single machine scheduling problem to minimize the weighted sum of completion times under precedence constraints in a series of recent papers it was established that this scheduling problem is a special case of minimum weighted vertex cover in this paper we show that the vertex cover graph associated with the scheduling problem is exactly the graph of incomparable pairs defined in the dimension theory of partial orders exploiting this relationship allows us to present a framework for obtaining 2 2 f approximation algorithms provided that the set of precedence constraints has fractional dimension of at most f our approach yields the best known approximation ratios for all previously considered special classes of precedence constraints and it provides the first results for bounded degree and orders of interval dimension 2 on the negative side we show that the addressed problem remains np hard even when restricted to the special case of interval orders furthermore we prove that the general problem if a fixed cost present in all feasible schedules is ignored becomes as hard to approximate as vertex cover we conclude by giving the first inapproximability result for this problem showing under a widely believed assumption that it does not admit a polynomial time approximation scheme

hard constraint satisfaction problems have hard gaps at location 1 an instance of the maximum constraint satisfaction problem max csp is a finite collection of constraints on a set of variables and the goal is to assign values to the variables that maximises the number of satisfied constraints max csp captures many well known problems such as maxk sat and max cut and is consequently np hard thus it is natural to study how restrictions on the allowed constraint types or constraint language affect the complexity and approximability of max csp the pcp theorem is equivalent to the existence of a constraint language for which max csp has a hard gap at location 1 i e it is np hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable all constraint languages for which the csp problem i e the problem of deciding whether all constraints can be satisfied is currently known to be np hard have a certain algebraic property we prove that any constraint language with this algebraic property makes max csp have a hard gap at location 1 which in particular implies that such problems cannot have a ptas unless p np we then apply this result to max csp restricted to a single constraint type this class of problems contains for instance max cut and max dicut assuming p np we show that such problems do not admit ptas except in some trivial cases our results hold even if the number of occurrences of each variable is bounded by a constant finally we give some applications of our results

np completeness and apx completeness of restrained domination in graphs let g v e be a simple graph a vertex set email protected v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in v s in this paper we investigate the np completeness of the restrained domination problem in planar graphs and split graphs meanwhile it is proved that the restrained domination problem is apx complete for bounded degree graphs

a hierarchy of near optimal policies for multistage adaptive optimization in this paper we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty applicable to multistage robust optimization and stochastic programming we introduce a hierarchy of near optimal polynomial disturbance feedback control policies and show how these can be computed by solving a single semidefinite programming problem the approach yields a hierarchy parameterized by a single variable the degree of the polynomial policies which controls the trade off between the optimality gap and the computational requirements we evaluate our framework in the context of three classical applications two in inventory management and one in robust regulation of an active suspension system in which very strong numerical performance is exhibited at relatively modest computational expense

the within strip discrete unit disk cover problem we present a study of the within strip discrete unit disk cover wsdudc problem which is a restricted version of the discrete unit disk cover dudc problem for the wsdudc problem there exists a set of points and a set of unit disks in the plane and the points and disk centres are conned to a strip of xed height an optimal solution to the wsdudc problem is a set of disks of minimum cardinality that covers all points in the input set we describe a range of approximation algorithms for the problem including 4 and 3 approximate algorithms which apply for strips of height 2 p 2 3 0 94 and 0 8 units respectively as well as a general scheme for any strip with less than unit height we prove that the wsdudc problem is np complete on strips of any xed height which is our most interesting result from a theoretical standpoint the result is also quite surprising since a number of similar problems are tractable on strips of xed height finally we discuss how these results may be applied to known dudc approximation algorithms

robust nonlinear optimization with conic representable uncertainty set the robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints this methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty in this paper the robust optimization methodology is applied to the general nonlinear programming nlp problem involving both uncertain inequality and equality constraints the uncertainty set is defined by conic representable sets the proposed uncertainty set is general enough to include many uncertainty sets which have been used in literature as special cases the robust counterpart rc of the general nlp problem is approximated under this uncertainty set it is shown that the resulting approximate rc of the general nlp problem is valid in a small neighborhood of the nominal value furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far the resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems

supermodularity and affine policies in dynamic robust optimization this paper considers a particular class of dynamic robust optimization problems where a large number of decisions must be made in the first stage which consequently fix the constraints and cost structure underlying a one dimensional linear dynamical system we seek to bridge two classical paradigms for solving such problems namely 1 dynamic programming dp and 2 policies parameterized in model uncertainties also known as decision rules obtained by solving tractable convex optimization problems we show that if the uncertainty sets are integer sublattices of the unit hypercube the dp value functions are convex and supermodular in the uncertain parameters and a certain technical condition is satisfied then decision rules that are affine in the uncertain parameters are optimal we also derive conditions under which such rules can be obtained by optimizing simple i e linear objective functions over the uncertainty sets our results suggest new modeling paradigms for dynamic robust optimiz

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

completeness in approximation classes we introduce a formal framework for studying approximation properties of np optimization npo problems the classes we consider are those appearing in the literature namely the class of approximable problems within a constant e apx the class of problems having a polynomial time approximation scheme pas and the class of problems having a fully polynomial time approximation scheme fpas we define natural approximation preserving reductions and obtain completeness results for these classes a complete problem in a class can not have stronger approximation properties unless p np we also show that the degree structure of npo allows intermediate degrees that is if p np there are problems which are neither complete nor belong to a lower class

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

robustness and regularization of support vector machines we consider regularized support vector machines svms and show that they are precisely equivalent to a new robust optimization formulation we show that this equivalence of robust optimization and regularization has implications for both algorithms and analysis in terms of algorithms the equivalence suggests more general svm like algorithms for classification that explicitly build in protection to noise and at the same time control overfitting on the analysis front the equivalence of robustness and regularization provides a robust optimization interpretation for the success of regularized svms we use this new robustness interpretation of svms to give a new proof of consistency of kernelized svms thus establishing robustness as the reason regularized svms generalize well

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

design of near optimal decision rules in multistage adaptive mixed integer optimization in recent years decision rules have been established as the preferred solution method for addressing computationally demanding multistage adaptive optimization problems despite their success existing decision rules a are typically constrained by their a priori design and b do not incorporate in their modeling adaptive binary decisions to address these problems we first derive the structure for optimal decision rules involving continuous and binary variables as piecewise linear and piecewise constant functions respectively we then propose a methodology for the optimal design of such decision rules that have a finite number of pieces and solve the problem robustly using mixed integer optimization we demonstrate the effectiveness of the proposed methods in the context of two multistage inventory control problems we provide global lower bounds and show that our approach is i practically tractable and ii provides high quality solutions that outperform alternative methods

some apx completeness results for cubic graphs four fundamental graph problems minimum vertex cover maximum independent set minimum dominating set and maximum cut are shown to be apx complete even for cubic graphs therefore unless p np these problems do not admit any polynomial time approximation scheme on input graphs of degree bounded by three

robust combinatorial optimization with variable cost uncertainty abstract we present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set we suppose here that the budget of uncertainty is given by a function of the problem variables yielding an uncertainty multifunction the new model is less conservative than the classical model and approximates better value at risk objective functions especially for vectors with few non zero components an example of budget function is constructed from the probabilistic bounds computed by bertsimas and sim we provide an asymptotically tight bound for the cost reduction obtained with the new model we turn then to the tractability of the resulting optimization problems we show that when the budget function is affine the resulting optimization problems can be solved by solving n 1 deterministic problems we propose combinatorial algorithms to handle problems with more general budget functions we also adapt existing dynamic programming algorithms to solve faster the robust counterparts of optimization problems which can be applied both to the traditional budgeted uncertainty model and to our new model we evaluate numerically the reduction in the price of robustness obtained with the new model on the shortest path problem and on a survivable network design problem

robust optimization of sums of piecewise linear functions with application to inventory problems robust optimization is a methodology that has gained a lot of attention in the recent years this is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models unfortunately the second property is usually lost when the cost function that needs to be robustified is not concave or linear with respect to the perturbing parameters in this paper we study robust optimization of sums of piecewise linear functions over polyhedral uncertainty set given that these problems are known to be intractable we propose a new scheme for constructing conservative approximations based on the relaxation of an embedded mixed integer linear program and relate this scheme to methods that are based on exploiting affine decision rules our new scheme gives rise to two tractable models that respectively take the shape of a linear program and a semidefinite program with the latter having the potential to provide solutions of better quality than the former at the price of heavie

high order difference methods for heat equations in polar cylindrical coordinates abstract fourth order difference methods for the solution of poisson equations in cylindrical polar coordinates are proposed the same technique is then applied to obtain o k 2 h 4 two level unconditionally stable adi methods for the solution of the heat equation in two dimensional polar coordinates and three dimensional cylindrical coordinates numerical examples given here show that the methods developed here retain their order and accuracy everywhere including the region in the vicinity of the singularity r 0

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

on approximating restricted cycle covers a cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle an l cycle cover is a cycle cover in which the length of every cycle is in the set l the weight of a cycle cover of an edge weighted graph is the sum of the weights of its edges we come close to settling the complexity and approximability of computing l cycle covers on the one hand we show that for almost all l computing l cycle covers of maximum weight in directed and undirected graphs is mathsf apx hard most of our hardness results hold even if the edge weights are restricted to zero and one on the other hand we show that the problem of computing l cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8 3 in the case of directed graphs this holds for arbitrary sets l

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

a family of single step houbolt time integration algorithms for structural dynamics a new family of implicit single step time integration methods is presented for solving structural dynamics problems the proposed method is unconditionally stable second order accurate and asymptotically annihilating it is spectrally equivalent to houbolt s method but is cast in single step form rather than multi step form thus the new algorithm computationally is more convenient an explicit predictor correcter algorithm is presented based upon the new implicit scheme the explicit algorithm is spectraily equivalent to the central difference method the two new algorithms are merged into an implicit explicit method resulting in an improved algorithm for solving structural dynamics problems composed of soft and stiff domains numerical results are presented demonstrating the improved performance of the new implicit explicit method compared to previously developed implicit explicit schemes for structural dynamics

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

a finite difference scheme for the heat conduction equation abstract a symmetrical semi implicit ssi difference scheme is formulated for the heat conduction equation the scheme is easy to code fast and quite accurate the advantage of the scheme appears mainly when used for large complicated multidimensional grids and for nonlinear problems

parallel scalable adjoint based adaptive solution of variable viscosity stokes flow problems we present a framework for parallel adaptive solution of variable viscosity stokes flow problems we focus on data structures algorithms and solvers that can scale to thousands of processor cores the problem is discretized by octree based finite elements with explicit enforcement of continuity constraints at hanging nodes the parallel octree structure allows for fast neighbor finding and facilitates local coarsening and refinement of the mesh mesh adaptivity is driven by a posteriori error indicators including adjoint based goal oriented techniques dynamic load balancing is achieved by dynamically partitioning a morton ordered space filling curve the stokes system is solved iteratively using the minimum residual method minres preconditioned by a schur complement based approximate inverse that employs algebraic multigrid v cycle approximations of the inverses of the poisson like operators we demonstrate the effectiveness of this framework on several testbed problems with up to 6 orders of magnitude variation in viscosity and up to 1 7 billion unknowns on up to 4096 cores the results indicate that the overhead due to all amr components is less than 3 of the overall solve time the solver exhibits very good algorithmic and parallel implementation scalability the solver is insensitive to the magnitude of viscosity variation and adjoint based adaptivity results in over two orders of magnitude reduction in number of unknowns and up to an order of magnitude improvement in runtime relative to a uniform mesh for the same level of error

finding approximate and constrained motifs in graphs one of the most relevant topics in the analysis of biological networks is the identification of functional motifs inside a network a recent approach introduced in literature called graph motif represents the network as a vertex colored graph and the motif m as a multiset of colors an occurrence of a motif m in a vertex colored graph g is a connected induced subgraph of g whose vertex set is colored exactly as m in this paper we investigate three different variants of the graph motif problem the first two variants minimum adding motif min add graph motif and minimum substitution motif min sub graph motif deal with approximate occurrences of a motif in the graph while the third variant constrained graph motif cgm constrains the motif to contain a given set of vertices we investigate the computational and parameterized complexity of the three problems we show that min add graph motifand min sub graph motifare both np hard even when m is a set and the graph is a tree with maximum degree 4 in which each color appears at most twice then we show that min sub graph motifis fixed parameter tractable when parameterized by the size of m finally we consider the parameterized complexity of the cgmproblem we give a fixed parameter algorithm for graphs of bounded treewidth and show that the problem is w 2 hard when parameterized by m even if the input graph has diameter 2

robust discrete optimization and network flows we propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution and is computationally tractable both practically and theoretically in particular when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation when only the cost coefficients are subject to uncertainty and the problem is a 0 1 discrete optimization problem on n variables then we solve the robust counterpart by solving at most n 1 instances of the original problem thus the robust counterpart of a polynomially solvable 0 1 discrete optimization problem remains polynomially solvable in particular robust matching spanning tree shortest path matroid intersection etc are polynomially solvable we also show that the robust counterpart of an np hard approximable 0 1 discrete optimization problem remains approximable finally we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network

gradient based optimization for poroelastic and viscoelastic mr elastography we describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography mre the algorithm can be considered as a generalized adjoint method based on a lagrangian formulation one requirement for the classic adjoint method is assurance of the self adjoint property of the stiffness matrix in the elasticity problem in this paper we show this property is no longer a necessary condition in our algorithm but the computational performance can be as efficient as the classic method which involves only two forward solutions and is independent of the number of parameters to be estimated the algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling various gradient and hessian based optimization techniques have been tested on simulation phantom and in vivo brain data the numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation

a novel parameterised approximation algorithm for minimum vertex cover parameterised approximation is a relatively new but growing field of interest it merges two ways of dealing with np hard optimisation problems namely polynomial approximation and exact parameterised exponential time algorithms we exemplify this idea by designing and analysing parameterised approximation algorithms for minimum vertex cover more specifically we provide a simple algorithm that works on any approximation ratio of the form 2l 1l 1 l 1 2 and has complexity that outperforms previously published algorithms based on sophisticated exact parameterised algorithms in particular for l 1 factor 1 5 approximation our algorithm runs in time o 1 0883 k where parameter k 23 t and t is the size of a minimum vertex cover additionally we present an improved polynomial time approximation algorithm for graphs of average degree at most four and a limited number of vertices with degree less than two

a value function based exact approach for the bilevel mixed integer programming problem we examine bilevel mixed integer programs whose constraints and objective functions depend on both upper and lower level variables the class of problems we consider allows for nonlinear terms to appear in both the constraints and the objective functions requires all upper level variables to be integer and allows a subset of the lower level variables to be integer this class of bilevel problems is difficult to solve because the upper level feasible region is defined in part by optimality conditions governing the lower level variables which are difficult to characterize because of the nonconvexity of the follower problem we propose an exact finite algorithm for these problems based on an optimal value function reformulation we demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior computational experiments demonstrate that our approach outperforms a state of the art algorithm for solving bilevel mixed integer linear programs

graph orientation with splits abstract the minimum maximum outdegree problem mmo is to assign a direction to every edge in an input undirected edge weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible in this paper we introduce a new variant of mmo called the p split minimum maximum outdegree problem p split mmo in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges for some specified non negative integer p and study its computational complexity

hardness of approximating flow and job shop scheduling problems we consider several variants of the job shop problem that is a fundamental and classical problem in scheduling the currently best approximation algorithms have worse than logarithmic performance guarantee but the only previously known inapproximability result says that it is np hard to approximate job shops within a factor less than 5 4 closing this big approximability gap is a well known and long standing open problem this article closes many gaps in our understanding of the hardness of this problem and answers several open questions in the literature it is shown the first nonconstant inapproximability result that almost matches the best known approximation algorithm for acyclic job shops the same bounds hold for the general version of flow shops where jobs are not required to be processed on each machine similar inapproximability results are obtained when the objective is to minimize the sum of completion times it is also shown that the problem with two machines and the preemptive variant with three machines have no ptas

the l diversity problem tractability and approximability publishing personal data without giving up privacy is becoming an increasingly important problem in different fields in the last years different interesting approaches have been proposed i e k anonymity and l diversity given an input table these approaches partition its rows so that the computed partition satisfies some constraint in order to prevent the inference of the individuals the data belong to then the rows in a same set of the partition are related to the same rows by suppressing some of their entries here we focus on the l diversity problem where the attributes of the input table are distinguished in sensitive attributes and quasi identifier attributes the goal is to partition the rows of the input table so that each set c of the partition contains at most 1l c rows having a specific value in the sensitive attribute and the number of suppressions is minimized in this paper we investigate the approximation and parameterized complexity ofl diversity first we prove that the problem is not approximable within factor clnl for some constant c 0 even if the input table consists of only two columns and that the problem is apx hard even if l 4 and the input table contains exactly three columns then we give an approximation algorithm of factor m where m 1 is the number of columns in the input table when the sensitive attribute ranges over an alphabet of constant size concerning the parameterized complexity we prove that the problem is w 1 hard when parameterized by the cost bound by l and by the size of the alphabet then we prove that the problem admits a fixed parameter algorithm when both the maximum number of different values in a column and the number of columns are parameters

uncertain linear programs extended affinely adjustable robust counterparts in this paper we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature in which recourse decisions are restricted to be linear in terms of the primitive uncertainties we propose a special case of the extended affinely adjustable robust counterpart the splitting based extended affinely adjustable robust counterpart and illustrate both theoretically and computationally that the potential of the affinely adjustable robust counterpart method is well beyond the one presented in the literature similar to the affinely adjustable robust counterpart our approach ends up with deterministic optimization formulations that are tractable and scalable to multistage problems

comparing incomplete sequences via longest common subsequence abstract inspired by scaffold filling a recent approach for genome reconstruction from incomplete data we consider a variant of the well known longest common subsequence problem for the comparison of two sequences the new problem called longest filled common subsequence aims to compare a complete sequence with an incomplete one i e with some missing elements longest filled common subsequence lfcs given a complete sequence a an incomplete sequence b and a multiset m of symbols missing in b asks for a sequence b obtained by inserting the symbols of m into b so that b induces a common subsequence with a of maximum length we investigate the computational and approximation complexity of the problem and we show that it is np hard and apx hard when a contains at most two occurrences of each symbol and we give a polynomial time algorithm when the input sequences are over a constant size alphabet we give a 3 5 approximation algorithm for the longest filled common subsequence problem finally we present a fixed parameter algorithm for the problem when it is parameterized by the number of symbols inserted in b that match symbols of a

on the tractability of finding disjoint clubs in a network abstract we study a variant of the problem of finding a collection of disjoint s clubs in a given network given a graph the problem asks whether there exists a collection of at most r disjoint s clubs that covers at least k vertices of the network an s club is a connected graph that has diameter bounded by s for a positive integer s we demand that each club is non trivial that is it has order at least t 2 for some positive integer t we prove that the problem is apx hard even when the input graph has bounded degree s 2 t 3 and r v moreover we show that the problem is polynomial time solvable when s 4 t 3 and r v and when s 3 t 2 and r v finally for s 2 we present a fixed parameter algorithm for the problem when parameterized by the number of covered vertices

robust counterparts of inequalities containing sums of maxima of linear functions abstract this paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions these problems include many practical problems e g problems with sums of absolute values and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables affine in a parameter with box uncertainty and affine in a parameter with general uncertainty in the literature often the reformulation is used that is exact when there is no uncertainty however in robust optimization this reformulation gives an inferior solution and provides a pessimistic view we observe that in many papers this conservatism is not mentioned some papers have recognized this problem but existing solutions are either conservative or their performance for different uncertainty regions is not known a comparison between them is not available and they are restricted to specific problems we describe techniques for general problems and compare them with numerical examples in inventory management regression and brachytherapy based on these examples we give recommendations for reducing the conservatism

measurement of viscoelastic properties of homogeneous soft solid using transient elastography an inverse problem approach two main questions are at the center of this paper the first one concerns the choice of a rheological model in the frequency range of transient elastography sonoelasticity or nmr elastography for soft solids 20 1000 hz transient elastography experiments based on plane shear waves that propagate in an agar gelatin phantom or in bovine muscles enable one to quantify their viscoelastic properties the comparison of these experimental results to the prediction of the two simplest rheological models indicate clearly that voigt s model is the better the second question studied in the paper deals with the feasibility of quantitative viscosity mapping using inverse problem algorithm in the ideal situation where plane shear waves propagate in a sample a simple inverse problem based on the helmholtz equation correctly retrieves both elasticity and viscosity in a more realistic situation with nonplane shear waves this simple approach fails nevertheless it is shown that quantitative viscosity mapping is s

full waveform inversion in three dimensional pml truncated elastic media abstract we are concerned with high fidelity subsurface imaging of the soil which commonly arises in geotechnical site characterization and geophysical explorations specifically we attempt to image the spatial distribution of the lame parameters in semi infinite three dimensional arbitrarily heterogeneous formations using surficial measurements of the soil s response to probing elastic waves we use the complete waveform response of the medium to drive the inverse problem by using a partial differential equation pde constrained optimization approach directly in the time domain to minimize the misfit between the observed response of the medium at select measurement locations and a computed response corresponding to a trial distribution of the lame parameters we discuss strategies that lend algorithmic robustness to our proposed inversion scheme to limit the computational domain to the size of interest we employ perfectly matched layers pmls in order to resolve the forward problem we use a recently developed hybrid finite element approach where a displacement stress formulation for the pml is coupled to a standard displacement only formulation for the interior domain thus leading to a computationally cost efficient scheme time integration is accomplished by using an explicit runge kutta scheme which is well suited for large scale problems on parallel computers we verify the accuracy of the material gradients obtained via our proposed scheme and report numerical results demonstrating successful reconstruction of the two lame parameters for both smooth and sharp profiles

tissue elasticity reconstruction using linear perturbation method a new method to reconstruct the elastic modulus of soft tissue subjected to an external static compression is presented in this approach the newton raphson method is used to vary a finite element fe model of the elasticity equations to fit in a least squared sense a set of axial tissue displacement fields estimated using a correlation technique applied to ultrasound signals the ill conditioning of the hessian matrix is eliminated using the tikhonov regularization technique this regularization provides a compromise between fidelity to the observed data and a priori information of the solution using an echographic image formation model it is shown that the method converges within a few iterations 8 10 and that strain images artifacts which are common in elastography are significantly reduced after the resolution of the inverse problem

spectral element technique for efficient parameter identification of layered media part iii viscoelastic aspects this article addresses the issues of wave propagation in elastic viscoelastic layered systems and viscous parameter identification from non destructive dynamic tests a methodology that combines the spectral element technique for the simulation of wave propagation with the differential operator technique for stress strain relationship in viscoelastic materials is adopted the compatibility between the two techniques stems from the fact that both can be treated in the frequency domain which enables naturally the adoption of fourier superposition the mathematical formulation of spectral elements for burger s viscoelastic material model is highlighted also an inverse procedure for the identification of the material s young s moduli and complex moduli for layer systems is described it is shown that the proposed methodology enables the substitution of an expensive laboratory testing procedure for the determination of material complex moduli with non destructive dynamic testing 2002 elsevier science ltd all rights reserved

complexity analysis of p 3 convexity problems on bounded degree and planar graphs this paper studies new complexity aspects of p 3 convexity restricted to planar graphs with bounded maximum degree more specifically we are interested in identifying either a minimum p 3 geodetic set or a minimum p 3 hull set of such graphs from which the whole vertex set of g is obtained either after one or sufficiently many iterations respectively each iteration adds to a set s all vertices of v g s with at least two neighbors in s in this paper it is shown that a minimum p 3 hull set of a graph g can be found in polynomial time when g n g c for some constant c deciding if there is a p 3 hull set of size at most k in a given graph remains np complete even for planar graphs with maximum degree four and surprisingly as well as rather counterintuitively it is np complete to decide if there is a p 3 hull set of size at most k in a graph with maximum degree three though one can determine a minimum p 3 hull set in polynomial time not only for cubic graphs but also for graphs with minimum feedback vertex set of bounded size and no vertices of degree two concerning p 3 geodetic sets the problem of deciding if there is a p 3 geodetic set of size at most k in a planar graph with maximum degree three is proved to be np complete finally from a parameterized point of view we observe that finding a p 3 geodetic set of size at most k where k is the parameter is w2 hard however when considering the maximum degree as an additional parameter this problem becomes fixed parameter tractable

high order difference methods for linear variable coefficient parabolic equation abstract in this paper we derive o k 2 h 4 two level three point finite difference methods for the solution of the general linear variable coefficient parabolic equation in one dimension u t a x u xx b x u x c x u 0 x 1 t 0 under suitable initial and boundary conditions the stability of the new schemes is examined using a linear stability analysis in particular we derive unconditionally stable o k 2 h 4 methods for the solution of the convection diffusion type equation in cylindrical and spherical coordinates viz u t u xx x u x cu 0

hardness results and approximation algorithms for weighted paired domination in graphs let g v e be a simple graph without isolated vertices a vertex set s v is a paired dominating set if every vertex in v s has a neighbor in s and the induced subgraph g s has a perfect matching in this paper we investigate the approximation hardness of paired domination in graphs for weighted paired domination an approximation algorithm in general graphs and an exact dynamic programming style algorithm in trees are also given

the label cut problem with respect to path length and label frequency given a graph with labels defined on edges and a source sink pair s t the label s t cut problem asks for a minimum number of labels such that the removal of edges with these labels disconnects s and t similarly the global label cut problem asks for a minimum number of labels to disconnect g itself for these two problems we identify two useful parameters i e l max the maximum length of any s t path only applies to label s t cut and f max the maximum number of appearances of any label in the graph applies to the two problems we show that l max 2 and f max 2 are two complexity thresholds for label s t cut furthermore we give i an o c k time parameterized algorithm for label s t cut with l max bounded from above where parameter k is the number of labels in a solution and c is a constant with l max 1 c l max ii a combinatorial l max approximation algorithm for label s t cut and iii a polynomial time exact algorithm for global label cut with f max bounded from above we give an fpt algorithm for label s t cut in a special case we give a pure combinatorial approximation algorithm for label s t cut we give a polynomial time exact algorithm for global label cut in a special case

theoretical limitations of the elastic wave equation inversion for tissue elastography this article examines the theoretical limitations of the local inversion techniques for the measurement of the tissue elasticity most of these techniques are based on the estimation of the phase speed or the algebraic inversion of a one dimensional wave equation to analyze these techniques the wave equation in an elastic continuum is revisited it is proven that in an infinite medium harmonic shear waves can travel at any phase speed greater than the classically known shear wave speed by demonstrating this for a special case with cylindrical symmetry hence in addition to the mechanical properties of the tissue the phase speed depends on the geometry of the wave as well the elastic waves in an infinite cylindrical rod are studied it is proven that multiple phase speeds can coexist for a harmonic wave at a single frequency this shows that the phase speed depends not only on the mechanical properties of the tissue but also on its shape the final conclusion is that the only way to avoid theore

max ones generalized to larger domains we study a family of problems called maximum solution where the objective is to maximize a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints when the domain is boolean i e restricted to 0 1 the maximum solution problem is identical to the well studied max ones problem and the approximability is completely understood for all restrictions on the underlying constraints s khanna m sudan l trevisan and d p williamson siam j comput 30 2001 pp 1863 1920 we continue this line of research by considering domains containing more than two elements we present two main results a complete classification for the approximability of all maximal constraint languages over domains of cardinality at most 4 and a complete classification of the approximability of the problem when the set of allowed constraints contains all permutation constraints under the assumption that a conjecture due to szczepara minimal clones generated by groupoids ph d thesis universite de montreal montreal qc 1996 holds we give a complete classification for all maximal constraint languages these classes of languages are well studied in universal algebra and computer science they have for instance been considered in connection with machine learning and constraint satisfaction our results are proved by using algebraic results from clone theory and the results indicate that this approach is very powerful for classifying the approximability of certain optimization problems

finding a potential community in networks abstract an independent 2 clique of a graph is a subset of vertices that is an independent set and such that any two vertices inside have a common neighbor outside in this paper we study the complexity of finding an independent 2 clique of maximum size in several graph classes and we compare it with the complexity of maximum independent set we prove that this problem is np hard on apex graphs apx hard on line graphs not n 1 2 approximable on bipartite graphs and not n 1 approximable on split graphs while it is polynomial time solvable on graphs of bounded degree and their complements graphs of bounded treewidth planar graphs c 3 c 6 free graphs threshold graphs interval graphs and cographs

the complexity and approximability of finding maximum feasible subsystems of linear relations we study the combinatorial problem which consists given a system of linear relations of finding a maximum feasible subsystem that is a solution satisfying as many relations as possible the computational complexity of this general problem named max fls is investigated for the four types of relations and various constrained versions of max fls where a subset of relations must be satisfied or where the variables take bounded discrete values are also considered we establish the complexity of solving these problems optimally and whenever they are intractable we determine their degree of approximability max fls with or relations is np hard even when restricted to homogeneous systems with bipolar coefficients whereas it can be solved in polynomial time for relations with real coefficients the various np hard versions of max fls belong to different approximability classes depending on the type of relations and the additional constraints we show that the range of approximability stretches from apx complete problems which can be approximated within a constant but not within every constant unless p np to npo pb complete ones that are as hard to approximate as all np optimization problems with polynomially bounded objective functions while max fls with equations and integer coefficients cannot be approximated within pe for some e 0 where p is the number of relations the same problem over gf q for a prime q can be approximated within q but not within qe for some e 0 max fls with strict or nonstrict inequalities can be approximated within 2 but not within every constant factor our results also provide strong bounds on the approximability of two variants of max fls with and relations that arise when training perceptrons which are the building blocks of artificial neural networks and when designing linear classifiers

algorithmic aspects of semitotal domination in graphs abstract for a graph g v e a set d v is called a semitotal dominating set of g if d is a dominating set of g and every vertex in d is within distance 2 of another vertex of d the minimum semitotal domination problem is to find a semitotal dominating set of minimum cardinality given a graph g and a positive integer k the semitotal domination decision problem is to decide whether g has a semitotal dominating set of cardinality at most k the semitotal domination decision problem is known to be np complete for general graphs in this paper we show that the semitotal domination decision problem remains np complete for planar graphs split graphs and chordal bipartite graphs we give a polynomial time algorithm to solve the minimum semitotal domination problem in interval graphs we show that the minimum semitotal domination problem in a graph with maximum degree admits an approximation algorithm that achieves the approximation ratio of 2 3 ln 1 showing that the problem is in the class log apx we also show that the minimum semitotal domination problem cannot be approximated within 1 ln v for any 0 unless np dtime v o log log v finally we prove that the minimum semitotal domination problem is apx complete for bipartite graphs with maximum degree 4

an inverse model and mathematical solution for inferring viscoelastic properties and dynamic deformations of heterogeneous structures abstract we proposed an adjoint based inverse method and mathematical solutions using lagrange multiplier theorem for inferring dynamic viscoelastic properties of heterogeneous structures with displacement observations to improve computation reliability and efficiency existing methods such as the one using finite difference approximated gradient may not be efficient and accurate enough for considering complex situations of the coupled effects of dynamic loading material deformation memory and structural heterogeneity the proposed method derives both gradient and hessian mathematically to satisfy the first order necessary and second order sufficient optimal conditions which has great advantages compared to other approaches we also proposed robust numerical algorithms for accurate and fast computations including a regularization to control reasonable parameter ranges a newton s method with hessian function to determine search direction for fast convenience and a modified armijo rule to find a stable step length we developed a galerkin time domain finite element method for numerical solutions of resulting partial differential equations and validated the model for a layered structure under dynamic loading tests results indicate that the proposed method has greatly improved computation accuracy and speed as compared to existing approaches it may be applied to a broad range of heterogeneous materials and structures at different length and time scales

the approximability of max csp with fixed value constraints in the maximum constraint satisfaction problem max csp one is given a finite collection of possibly weighted constraints on overlapping sets of variables and the goal is to assign values from a given finite domain to the variables so as to maximize the number or the total weight for the weighted case of satisfied constraints this problem is np hard in general and therefore it is natural to study how restricting the allowed types of constraints affects the approximability of the problem in this article we show that any max csp problem with a finite set of allowed constraint types which includes all fixed value constraints i e constraints of the form x e a is either solvable exactly in polynomial time or else is apx complete even if the number of occurrences of variables in instances is bounded moreover we present a simple description of all polynomial time solvable cases of our problem this description relies on the well known algebraic combinatorial property of supermodularity

methods of interconversion between linear viscoelastic material functions part i a numerical method based on prony series abstract an efficient and accurate numerical method of interconversion between linear viscoelastic material functions based on a prony series representation is presented and tested using experimental data from selected polymeric materials the method is straightforward and applicable to interconversion between modulus and compliance functions in time frequency and laplace transform domains good agreement is shown between solutions obtained from the method in different domains a detailed computational procedure and selection of values for parameters involved in the method are presented and illustrated in particular the effects of different choices of relaxation and retardation times on the accuracy of the method are discussed the mathematical efficiency associated with prony series representations of both source and target transient material functions is fully utilized the method is general enough to cover both viscoelastic solids and liquids the tensile relaxation data from polymethyl methacrylate pmma and the shear storage compliance data from polyisobutylene are used in illustrating the method in a companion paper schapery and park 1998 an extended approximate analytical interconversion method is presented

a dynamic programming approach for a class of robust optimization problems common approaches to solve a robust optimization problem decompose the problem into a master problem mp and adversarial separation problems aps mp contains the original robust constraints however written only for finite numbers of scenarios additional scenarios are generated on the fly by solving the aps we consider in this work the budgeted uncertainty polytope from bertsimas and sim widely used in the literature and propose new dynamic programming algorithms to solve the aps that are based on the maximum number of deviations allowed and on the size of the deviations our algorithms can be applied to robust constraints that occur in various applications such as lot sizing tsp with time windows scheduling problems and inventory routing problems among many others we show how the simple version of the algorithms leads to a fptas when the deterministic problem is convex we assess numerically our approach on a lot sizing problem showing a comparison with the classical mip reformulation of the ap

semiconductor lot allocation using robust optimization abstract in this work the problem of allocating a set of production lots to satisfy customer orders is considered this research is of relevance to lot to order matching problems in semiconductor supply chain settings we consider that lot splitting is not allowed during the allocation process due to standard practices furthermore lot sizes are regarded as uncertain planning data when making the allocation decisions due to potential yield loss in order to minimize the total penalties of demand un fulfillment and over fulfillment a robust mixed integer optimization approach is adopted to model is proposed the problem of allocating a set of work in process lots to customer orders where lot sizes are modeled using ellipsoidal uncertainty sets to solve the optimization problem efficiently we apply the techniques of branch and price and benders decomposition the advantages of our model are that it can represent uncertainty in a straightforward manner with little distributional assumptions and it can produce solutions that effectively hedge against the uncertainty in the lot sizes using very reasonable amounts of computational effort

on the hardness of finding near optimal multicuts in directed acyclic graphs abstract given an edge weighted di graph and a list of source sink pairs of vertices of this graph the minimum multicut problem consists in selecting a minimum weight set of edges or arcs whose removal leaves no path from each source to the corresponding sink this is a well known np hard problem and improving several previous results we show that it remains apx hard in unweighted directed acyclic graphs dag even with only two source sink pairs this is also true if we remove vertices instead of arcs

complexity issues in color preserving graph embeddings in the context of comparative analysis of protein protein interaction graphs we use a graph based formalism to detect the preservation of a given protein complex pattern graph in the protein protein interaction graph target graph of another species with respect to w r t orthologous proteins we give an efficient exponential time randomized algorithm in case the occurrence of the pattern graph in the target graph is required to be exact for approximate occurrences we prove a tight inapproximability result and give four approximation algorithms that deal with bounded degree graphs small ortholog numbers linear forests and very simple yet hard instances respectively