radial solutions of δu f u 0 with prescribed numbers of zeros u 0 0 u r f 0 as r 03 1 2 here n 1 is a real parameter and the function f satisfies the following hypotheses f 1 f r r is locally lipschitz continuous f2 uf u 0 and j 0 such that f u 0 on 0 pi f u 0 on uc 0 f u 0 on b 01 f u 0 on a pi where f u f r f s ds f4 f u k u jujp u g u where

a sum of disjoint products algorithm for reliability evaluation of flow networks abstract this paper proposes a revised algorithm to evaluate the unreliability of a flow network in which capacities of arcs are assumed to be independent binary valued random variables such a problem is a generalization of the well known np hard two terminal reliability problem which evaluates the probability of the connection from a source node to a sink node the proposed algorithm is motivated by rueger both in a branching manner the proposed and rueger s algorithms express the system unreliability in terms of a sum of disjoint products where each product is derived from a branching condition b via a d cutb in o m log m time and via the first system failure under b in o d n2 2m time respectively where d is the demand n and m are the numbers of nodes and arcs in the network respectively experimental experiences show that the proposed algorithm drastically reduces the execution time and performs more robustly when compare to rueger s algorithm but the number of disjoint products derived by it will be a little bit larger

use of dynamic trees in a network simplex algorithm for the maximum flow problem goldfarb and hao 1990 have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann vertex m arc network in at mostnm pivots and o n 2 m time in this paper we describe how to extend the dynamic tree data structure of sleator and tarjan 1983 1985 to reduce the running time of this algorithm to o nm logn this bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem our extension of dynamic trees is interesting in its own right and may well have additional applications

computing network reliability in time polynomial in the number of cuts we present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network the computation time of this algorithm is bounded by a polynomial in the number of s t cuts in the network we also examine the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network these problems are distinguished as either having algorithms that are polynomial in the number of such sets or having no such algorithms unless p np

approximation algorithms for single source unsplittable flow in the single source unsplittable flow problem we are given a network g a source vertex s and k commodities with sinks ti and real valued demands rho i 1 leq i leq k we seek to route the demand rho i of each commodity i along a single s ti flow path so that the total flow routed across any edge e is bounded by the edge capacity ue the conceptual difficulty of this np hard problem arises from combining packing constraints due to the existence of capacities with path selection in a graph of arbitrary topology in this paper we give a generic framework which yields approximation algorithms that are simpler than those previously known and achieve significant improvements upon the approximation ratios our framework with appropriate subroutines applies to all optimization versions previously considered and unlike previous work treats in a unified manner directed and undirected graphs we provide extensions of our algorithms which yield the best possible approximation guarantees for restricted sets of demand values and an associated scheduling problem

an equivalent relationship in discrete dynamical systems an equivalent relationship between the generalized ergodicity almost everywhere e chain transitivity and the domain of influence of an invariant set for a discrete dynamical system on a compact metric space is explored a necessary and sufficient condition for an invariant set to be a periodic orbit is given

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

phase unwrapping via graph cuts phase unwrapping is the inference of absolute phase from modulo 2pi phase this paper introduces a new energy minimization framework for phase unwrapping the considered objective functions are first order markov random fields we provide an exact energy minimization algorithm whenever the corresponding clique potentials are convex namely for the phase unwrapping classical lp norm with pges1 its complexity is kt n 3n where k is the length of the absolute phase domain measured in 2pi units and t n m is the complexity of a max flow computation in a graph with n nodes and m edges for nonconvex clique potentials often used owing to their discontinuity preserving ability we face an np hard problem for which we devise an approximate solution both algorithms solve integer optimization problems by computing a sequence of binary optimizations each one solved by graph cut techniques accordingly we name the two algorithms puma for phase unwrapping max flow min cut a set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state of the art phase unwrapping algorithms

faster algorithms for the quickest transshipment problem a transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves how can this be done in the minimum number of waves this is the question tackled in the quickest transshipment problem hoppe and tardos math oper res 25 2000 pp 36 62 describe the only known polynomial time algorithm to solve this problem they actually solve the significantly harder problem in which it takes a prespecified amount of time for flow to travel from one end of an arc to the other their algorithm repeatedly calls an oracle for submodular function minimization we present an algorithm that finds a quickest transshipment with a polynomial number of maximum flow computations and a faster algorithm that also uses minimum cost flow computations when there is only one sink we show how the algorithm can be sped up to return a solution using o k maximum flow computations where k is the number of sources hajek and ogier networks 14 1984 pp 457 487 describe an algorithm that finds a fractional solution to the single sink quickest transshipment problem on a network with n nodes and m arcs using o n maximum flow computations they actually solve the universally quickest transshipment a flow over time that minimizes the amount of supply left in the network at every moment of time in this paper we show how to solve the universally quickest transshipment in o mnlog n2 m time the same asymptotic time as a push relabel maximum flow computation

integer programming formulations for the elementary shortest path problem abstract given a directed graph g v a with arbitrary arc costs the elementary shortest path problem espp consists of finding a minimum cost path between two nodes s and t such that each node of g is visited at most once if negative costs are allowed the problem is np hard in this paper several integer programming formulations for the espp are compared we present analytical results based on a polyhedral study of the formulations and computational experiments where we compare their linear programming relaxation bounds and their behavior within a branch and cut framework the computational results show that a formulation with dynamically generated cutset inequalities is the most effective

the pseudoflow algorithm a new algorithm for the maximum flow problem we introduce the pseudoflow algorithm for the maximum flow problem that employs only pseudoflows and does not generate flows explicitly the algorithm solves directly a problem equivalent to the minimum cut problem the maximum blocking cut problem once the maximum blocking cut solution is available the additional complexity required to find the respective maximum flow is o m log n a variant of the algorithm is a new parametric maximum flow algorithm generating all breakpoints in the same complexity required to solve the constant capacities maximum flow problem the pseudoflow algorithm has also a simplex variant pseudoflow simplex that can be implemented to solve the maximum flow problem one feature of the pseudoflow algorithm is that it can initialize with any pseudoflow this feature allows it to reach an optimal solution quickly when the initial pseudoflow is close to an optimal solution the complexities of the pseudoflow algorithm the pseudoflow simplex and the parametric variants of pseudoflow and pseudoflow simplex algorithms are all o mn log n on a graph with n nodes and m arcs therefore the pseudoflow simplex algorithm is the fastest simplex algorithm known for the parametric maximum flow problem the pseudoflow algorithm is also shown to solve the maximum flow problem on s t tree networks in linear time where s t tree networks are formed by joining a forest of capacitated arcs with nodes s and t adjacent to any subset of the nodes

o sqrt logn approximation to sparsest cut in tilde o n 2 time this paper shows how to compute o sqrt log n approximations to the sparsest cut and balanced separator problems in tilde o n 2 time thus improving upon the recent algorithm of arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231 their algorithm uses semidefinite programming and requires tilde o n 9 5 time our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs the existence of expander flows was also established by arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231

polynomial time separation of a superclass of simple comb inequalities the comb inequalities are a well known class of facet inducing inequalities for the traveling salesman problem defined in terms of certain vertex sets called the handle and the teeth we say that a comb inequality is simple if the following holds for each tooth either the intersection of the tooth with the handle has cardinality one or the part of the tooth outside the handle has cardinality one or both the simple comb inequalities generalize the classical 2 matching inequalities of edmonds edmonds j 1965 maximum matching and a polyhedron with 0 1 vertices j res nat bur standards69b 125 130 and also the so called chvatal comb inequalities in 1982 padberg and rao padberg m w m r rao 1982 odd minimum cut sets and b matchings math oper res 7 67 80 gave a polynomial time separation algorithm for the 2 matching inequalities i e an algorithm for testing if a given fractional solution to an lp relaxation violates a 2 matching inequality we extend this significantly by giving a polynomial time separation algorithm for a class of valid inequalities which includes all simple comb inequalities

calculation of minimal capacity vectors through k minimal paths under budget and time constraints abstract reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink the quickest path problem thus arises to find a single path with minimum transmission time more specifically the capacity of each arc is assumed to be deterministic however in many real life networks such as computer networks and telecommunication networks the capacity of each arc is stochastic due to failure maintenance etc hence the minimum transmission time is not a fixed number such a network is named a stochastic flow network in order to reduce the transmission time the network allows the data to be transmitted through k minimal paths simultaneously including the cost attribute this paper evaluates the probability that d units of data can be transmitted under both time threshold t and budget b such a probability is called the system reliability an efficient algorithm is proposed to generate all of lower boundary points for d t b the minimal capacity vectors satisfying the demand time and budget requirements the system reliability can then be computed in terms of such points moreover the optimal combination of k minimal paths with highest system reliability can be obtained

a heuristic for blocking flow algorithms abstract this note presents a simple heuristic to speed up algorithms for the maximum flow problem that works by repeatedly finding blocking flows in layered acyclic networks the heuristic assigns a capacity to each vertex of the layered network which will be an upper bound on the amount of flow that can be transported through that vertex to the sink this information can be utilized when constructing a blocking flow since no vertex can ever accommodate more flow than its capacity the static heuristic computes capacities in a layered network once while a dynamic variant readjusts capacities during construction of the blocking flow the effects of both static and dynamic heuristics are evaluated by a series of experiments with the wave algorithm of tarjan although neither give theoretical improvement to the efficiency of the algorithm the practical effects are in most cases worthwhile and for certain types of networks quite dramatic

shape matching and modeling using skeletal context shape is a significant visual clue for human perception and shape models show considerable promise as a basis for extracting objects from images this paper proposes a novel approach for shape matching and modeling using the symmetry characterization of shape interior and the spatial relationships of shape structures based on the representative skeletal features we develop a mechanism to generate a coarse segment matching between different instances of an object additionally the natural correspondence of skeletal branches to sequential segments along the shape curves is employed in the matching process to avoid false correspondences across different segments point matches within the corresponding segments are then obtained by solving a constrained assignment problem the validation of the proposed approach is illustrated on various data sets in the presence of considerable deformation and occlusion and the results are compared with those of popular approaches we also demonstrate the performance of our method on biological objects for shape modeling showing better models than those obtained by the state of the art shape modeling approaches

a new algorithm for solving the feasibility problem of a network flow abstract a network d with the constraints of conservation and boundedness is given the feasibility problem is defined as is there a flow x satisfying the constraints in this paper we suppose that the lower and upper bounds are integers we first present a new theorem characterizing the conditions for feasibility and then describe a scaling algorithm to solve the problem our algorithm relaxes the capacity bounds and then successively reduces the value of relaxation if the network is infeasible then our algorithm not only diagnoses it and finds a positive cut but also gives a geometrical description to feasibility concept our algorithm also helps modeler to repair an infeasible network or to estimate the maximum cost of repairing for a network with n nodes and m arcs the algorithm runs in o m 2 log nu time where u is the largest absolute arc bounds

on dynamical systems with an integral invariant on the torus abstract differential systems on the torus with an integral invariant and containing singular points are considered the main topological types of global structure of trajectories for this class of differential equations are studied and a simple criterion to determine to which type any concrete differential system belongs is also given

on strongly polynomial dual simplex algorithms for the maximum flow problem several pivot rules for the dual network simplex algorithm that enable it to solve a maximum flow problem on an n node m arc network in at most 2nm pivots and o n 2 m time are presented these rules are based on the concept of a preflow and depend upon the use of node labels which are either the lengths of a shortest pseudoaugmenting path from those nodes to the sink node or valid underestimates of those lengths extended versions of our algorithms are shown to solve an important class of parametric maximum flow problems with no increase in the worst case pivot and time bounds of these algorithms

distribution and reliability evaluation of max flow in dynamic multi state flow networks abstract in this article each arc in multi state flow networks in addition to multi valued capacities and associated operation probabilities is weighted with a transit time as a result the value of max flow from source to sink within specified time horizon is multi valued existing literature evaluates the transit time integrated reliability with a restriction that data is transmitted through k disjoint minimal paths this article considers the same reliability problem however the transmission of data is extended from k disjoint minimal paths to a flow that includes all disjoint and non disjoint minimal paths simultaneously this paper presents an algorithm to evaluate the probability distribution of the values of dynamic max flow the expectation of dynamic max flow as a representation of the distribution can be induced directly the transit time integrated reliability r d t is then computed which is the probability that at least d unit of data can be transmitted from source to sink within time horizon t this study is the first that discusses transit time integrated reliability in terms of flow finally computational experiments are conducted on a benchmark network to explore the properties of the proposed algorithms

relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow this paper presents two new scaling algorithms for the minimum cost network flow problem one a primal cycle canceling algorithm the other a dual cut canceling algorithm both algorithms scale a relaxed optimality parameter and create a second inner relaxation the primal algorithm uses the inner relaxation to cancel a most negative node disjoint family of cycles w r t the scaled parameter the dual algorithm uses it to cancel most positive cuts w r t the scaled parameter we show that in a network with n nodes and m arcs both algorithms need to cancel only omn objects per scaling phase furthermore we show how to efficiently implement both algorithms to yield weakly polynomial running times that are as fast as any other cycle or cut canceling algorithms our algorithms have potential practical advantages compared to some other canceling algorithms as well along the way we give a comprehensive survey of cycle and cut canceling algorithms for min cost flow we also clarify the formal duality between cycles and cuts

parallel algorithms for minimum cuts and maximum flows in planar networks algorithms are given that compute maximum flows in planar directed networks either in o log n 3 parallel time using o n 4 processors or o log n 2 parallel time using o n 6 processors the resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow when such a value is given or when the computation is on an undirected network the bound is o log n 2 time using o n 3 processors no efficient parallel algorithm is known for the maximum flow problem in general networks

on a nonlinear bessel equation numerical power series and asymptotic solutions are presented for the differential equation f r 1 f f f 3 0 0 r infty which arises in connection with self focusing

self adjusting binary search trees the splay tree a self adjusting form of binary search tree is developed and analyzed the binary search tree is a data structure for representing tables and lists so that accessing inserting and deleting items is easy on an n node splay tree all the standard search tree operations have an amortized time bound of o log n per operation where by amortized time is meant the time per operation averaged over a worst case sequence of operations thus splay trees are as efficient as balanced trees when total running time is the measure of interest in addition for sufficiently long access sequences splay trees are as efficient to within a constant factor as static optimum search trees the efficiency of splay trees comes not from an explicit structural constraint as with balanced trees but from applying a simple restructuring heuristic called splaying whenever the tree is accessed extensions of splaying give simplified forms of two other data structures lexicographic or multidimensional search trees and link cut trees

greedy splitting algorithms for approximating multiway partition problems given a system v t f k where v is a finite set open image in new window is a submodular function and k 2 is an integer the general multiway partition problem mpp asks to find a k partition open image in new window v1 v2 vk of v that satisfiesopen image in new windowfor all i and minimizes f v1 f v2 f vk where open image in new window is a k partition of open image in new window hold mpp formulation captures a generalization in submodular systems of many np hard problems such as k way cut multiterminal cut target split and their generalizations in hypergraphs this paper presents a simple and unified framework for developing and analyzing approximation algorithms for various mpps

the nested chinese restaurant process and bayesian nonparametric inference of topic hierarchies we present the nested chinese restaurant process ncrp a stochastic process that assigns probability distributions to ensembles of infinitely deep infinitely branching trees we show how this stochastic process can be used as a prior distribution in a bayesian nonparametric model of document collections specifically we present an application to information retrieval in which documents are modeled as paths down a random tree and the preferential attachment dynamics of the ncrp leads to clustering of documents according to sharing of topics at multiple levels of abstraction given a corpus of documents a posterior inference algorithm finds an approximation to a posterior distribution over trees topics and allocations of words to levels of the tree we demonstrate this algorithm on collections of scientific abstracts from several journals this model exemplifies a recent trend in statistical machine learning the use of bayesian nonparametric methods to infer distributions on flexible data structures

stochastic flow networks via multiple paths under time threshold and budget constraint this paper extends the quickest path problem to a stochastic flow network in which the capacity of each arc is variable we mainly evaluate the system reliability that d units of data can be sent from the source to the sink under both time threshold t and budget b in particular the data are transmitted through multiple disjoint minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points by utilizing a union of subsets computational complexity in both worst case and average cases show that the proposed algorithm can be executed efficiently

lipschitz stability of nonlinear systems of differential equations in s the authors introduced the notion of lipschitz stability in differential equations this notion lies somewhere between uniform stability on one side and the notions of asymptotic stability in variation 3 and uniform stability in variation 4 on the other side however lipschitz stability is new only as a nonliner phenomenon since it coincides with uniform stability in linear systems s an important feature of lipschitz stability is that unlike uniform stability the linearized system inherits the property of lipschitz stability from the original nonlinear system 5 in this paper we pursue the study of lipschitz stability that started in s using essentially the techniques of liapunov functions then we give sufficient conditions for the lipschitz stability of certain nonlinearly pertur bed nonlinear systems such systems include among other equations certain integrodifferential and functional differential equations then we give an example which can be investigated successfully using our results but cannot be handled by any previous techniques or results 9

a new approach for computing a most positive cut using the minimum flow algorithms abstract the minimum flow problem is one of the network flow problems in which computes minimum flow from a source node s to a sink node t to this point the algorithms of the minimum flow problem have been only referred to solve certain examples like the machine setup problem in this paper we describe correspondence between the minimum flow problem and the most positive cut problem we present a new algorithm to solve the most positive cut problem using the minimum flow algorithms the running time of the algorithm is equal to one minimum flow computation also we prove that the infeasibility of a network can be distinguished by solving a minimum flow problem

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

remark on a system of two nonlinear differential equations we discuss qualitatively and numerically the solutions of a system of two nonlinear first order differential equations the computations supply only the fundamental mode which is also the mode of physical interest

decomposition of binary images a survey and comparison we present an overview of the most important methods that decompose an arbitrary binary object into a union of rectangles we describe a run length encoding and its generalization decompositions based on quadtrees on mathematical morphology on the distance transform and a theoretically optimal decomposition based on a maximal matching in bipartite graphs we compare their performance in image compression in moment computation and in linear filtering we show that the choice is always a compromise between the complexity and time memory consumption we give advice how to select an appropriate method in particular cases

fast and fine quickest path algorithm abstract we address the quickest path problem proposing a new algorithm based on the fact that its optimal solution corresponds to a supported non dominated point in the objective space of the minsum maxmin bicriteria path problem this result allows us to design a label setting algorithm which improves all existing algorithms in the state of the art as it is shown in the extensive experiments carried out considering synthetic and real networks

internet packet routing application of a k quickest path algorithm this paper describes a study on the application of an algorithm to rank the k quickest paths to the routing of data packets in internet networks for this purpose an experimental framework was developed by considering two types of random generated networks to simulate values of the ip packet sizes a truncated pareto distribution was defined having in mind to reflect a key feature of internet traffic namely its self similar stochastic nature results concerning the average cpu times of the algorithm for the different sets of experiments will be presented and discussed

lower bounds in a parallel model without bit operations we define a natural and realistic model of parallel computation called the pram model without bit operations it is like the usual pram model the main difference being that no bit operations are provided it encompasses virtually all known parallel algorithms for weighted combinatorial optimization and algebraic problems in this model we prove that for some large enough constant b the mincost flow problem for graphs with n vertices cannot be solved deterministically or with randomization in sqrt n b expected time using 2 sqrt n b processors this is so even if we restrict every cost and capacity to be an integer nonnegative if it is a capacity of bitlength at most an for some large enough constant a a similar lower bound is also proved for the max flow problem it follows that these problems cannot be solved in our model deterministically or with randomization in omega n c expected time with 2 omega n c processors where c is an appropriate positive constant and n is the total bitlength of the input since these problems were known to be p complete this provides concrete support for the belief that p completeness implies high parallel complexity and for the p not nc conjecture our lower bounds also extend to the pram model with limited bit operations which provides instructions for parity and left or right shift by one bit our proof is based on basic algebraic geometry so we investigate if the algebrogeometric approach could also work for the p versus nc problem our results support this possibility and a close analysis of the limitation of our technique in this context suggests that such a proof of p not nc should somehow use geometric invariant theory in a deep way

the quickest transshipment problem a dynamic network consists of a graph with capacities and transit times on its edges the quickest transshipment problem is de2ned by a dynamic network with several sources and sinks each source has a speci2ed supply and each sink has a specified demand the problem is to send exactly the right amount of 6ow out of each source and into each sink in the minimum overall time variations of the quickest transshipment problem have been studied extensively the special case of the problem with a single sink is commonly used to model building evacuation similar dynamic network flow problems have numerous other applications in some of these the capacities are small integers and it is important to find integral flows there are no polynomial time algorithms known for most of these problems in this paper we give the first polynomial time algorithm for the quickest transshipment problem our algorithm provides an integral optimum flow previously the quickest transshipment problem could only be solved efficiently in the special case of a single source and single sink

m convex function minimization by continuous relaxation approach proximity theorem and algorithm the concept of m convexity for functions in integer variables introduced by murota adv math 124 1996 pp 272 311 plays a primary role in the theory of discrete convex analysis in this paper we consider the problem of minimizing an m convex function which is a natural generalization of the separable convex resource allocation problem under a submodular constraint and contains some classes of nonseparable convex function minimization on integer lattice points we propose a new approach for m convex function minimization based on continuous relaxation by establishing proximity theorems we develop a new algorithm based on continuous relaxation we apply the approach to some special cases of the separable convex quadratic resource allocation problem and the convex quadratic tree resource allocation problem to obtain faster algorithms

practical sequential bounds for approximating two terminal reliability with increasing emphases on better and more reliable services network systems have incorporated reliability analysis as an integral part in their planning design and operation this article first presents a simple exact decomposition algorithm for computing the np hard two terminal reliability which measures the probability of successful communication from specified source node to sink node in the network then a practical bounding algorithm which is indispensable for large networks is presented by modifying the exact algorithm for obtaining sequential lower and upper bounds on two terminal reliability based on randomly generated large networks computational experiments are conducted to compare the proposed algorithm to the well known and widely used edge packing approximation model and to explore the performance of the proposed bounding algorithm computational results reveal that the proposed bounding algorithm is superior to the edge packing model and the trade off of accuracy for execution time ensures that an exact difference between upper and lower bounds on two terminal reliability can be obtained within an acceptable time

solving integer programs over monotone inequalities in three variables a framework for half integrality and good approximations abstract we define a class of monotone integer programs with constraints that involve up to three variables each a generic constraint in such integer program is of the form ax by z c where a and b are nonnegative and the variable z appears only in that constraint we devise an algorithm solving such problems in time polynomial in the length of the input and the range of variables u the solution is obtained from a minimum cut on a graph with o nu nodes and o mu arcs where n is the number of variables of the types x and y and m is the number of constraints our algorithm is also valid for nonlinear objective functions nonmonotone integer programs are optimization problems with constraints of the type ax by z c without restriction on the signs of a and b such problems are in general np hard we devise here an algorithm relying on a transformation to the monotone case that delivers half integral superoptimal solutions in polynomial time such solutions provide bounds on the optimum value that can only be superior to bounds provided by linear programming relaxation when the half integral solution can be rounded to an integer feasible solution this is a 2 approximate solution in that the technique is a unified 2 approximation technique for a large class of problems the results apply also for general integer programming problems with worse approximation factors that depend on a quantifier measuring how far the problem is from the class of problems we describe the algorithm described here has a wide array of problem applications an additional important consequence of our results is that nonmonotone problems in the framework are max snp hard and at least as hard to approximate as vertex cover problems that are amenable to the analysis provided here are easily recognized the analysis itself is entirely technical and involves manipulating the constraints and transforming them to a totally unimodular system while losing no more than a factor of 2 in the integrality

approximation algorithms for the discrete time cost tradeoff problem due to its obvious practical relevance the time cost tradeoff problem has attracted the attention of many researchers over the last forty years while the linear time cost tradeoff problem can be solved in polynomial time its discrete variant is known to be np hard we present the first approximation algorithms for the discrete time cost tradeoff problem specifically given a fixed budget we consider the problem of finding a shortest schedule for a project we give an approximation algorithm with performance ratio 3 2 for the class of projects where all feasible durations of activities are either 0 1 or 2 we extend our result by giving approximation algorithms with performance guarantee olog l where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity finally we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget

reliability evaluation of a revised stochastic flow network with uncertain minimum time abstract this paper constructs a revised stochastic flow network to model a realistic computer network in which each arc has a lead time and a stochastic capacity the minimum time to send a specified amount of data through the network is thus uncertain hence this paper mainly proposes an approach for evaluating the system reliability that d units of data can be transmitted through k minimal paths simultaneously within the time threshold t the idea of lower boundary points for d t the minimal system states satisfying the demand d within the time threshold t is proposed firstly all system states meeting the time and demand requirements can be represented as the union of subsets generated from all lower boundary points for d t and thus the system reliability is computed quickly

a dynamic bounding algorithm for approximating multi state two terminal reliability abstract this paper modifies jane and laih s 2008 exact and direct algorithm to provide sequences of upper bounds and lower bounds that converge to the np hard multi state two terminal reliability advantages of the modified algorithm include 1 it does not require a priori the lower and or upper boundary points of the network 2 it derives a series of increasing lower bounds and a series of decreasing upper bounds simultaneously guaranteed to enclose the exact reliability value and 3 trade off between accuracy and execution time can be made to ensure an exact difference between the upper and lower bounds within an acceptable time examples are analyzed to illustrate the bounding algorithm and to compare the bounding algorithm with existing algorithms computational experiments on a large network are conducted to realize the performance of the bounding algorithm

fast computation of bounds for two terminal network reliability in this paper an algorithm for the fast computation of network reliability bounds is proposed the evaluation of the network reliability is an intractable problem for very large networks and hence approximate solutions based on reliability bounds have assumed importance the proposed bounds computation algorithm is based on an efficient bdd representation of the reliability graph model and a novel search technique to find important minpaths mincuts to quickly reduce the gap between the reliability upper and lower bounds furthermore our algorithm allows the control of the gap between the two bounds by controlling the overall execution time therefore a trade off between prediction accuracy and computational resources can be easily made in our approach the numerical results are presented for large real example reliability graphs to show the efficacy of our approach

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

dynamic trees as search trees via euler tours applied to the network simplex algorithm thedynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges linking and splitting by deleting edges cutting while at the same time allowing reporting of certain combinations of vertex or edge values for many applications of dynamic trees values must be combined along paths for other applications values must be combined over entire trees for the latter situation an idea used originally in parallel graph algorithms to represent trees by euler tours leads to a simple implementation with a time of o logn per tree operation wheren is the number of tree vertices we apply this representation to the implementation of two versions of the network simplex algorithm resulting in a time of o logn per pivot wheren is the number of vertices in the problem network

on the complexity of nonnegative matrix scaling an n n nonnegative matrix a is said to be doubly stochastic scalable if there exist two positive diagonal matrices x and y such that xay is doubly stochastic we derive an upper bound on the norms of the scaling factors x and y and give a polynomial time complexity bound on the problem of computing the scaling factors to a prescribed accuracy

reliability and covariance estimation of weighted k out of n multi state systems abstract in the literature of reliability engineering reliability of the weighted k out of n system can be calculated using component reliability based on the structure function the calculation usually assumes that the true component reliability is completely known however this is not the case in practical applications instead component reliability has to be estimated using empirical sample data uncertainty arises during this estimation process and propagates to the system level this paper studies the propagation mechanism of estimation uncertainty through the universal generating function method equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived this is a unified approach it can be applied to weighted k out of n systems with multi state components to weighted k out of n systems with binary components and to simple series and parallel systems it may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems

time version of the shortest path problem in a stochastic flow network many studies on hardware framework and routing policy are devoted to reducing the transmission time for a flow network a time version of the shortest path problem thus arises to find a quickest path which sends a given amount of data from the unique source to the unique sink with minimum transmission time more specifically the capacity of each arc in the flow network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc should be stochastic due to failure maintenance etc such a network is named a stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent under the time constraint t such a probability is named the system reliability in particular the data are transmitted through two minimal paths simultaneously in order to reduce the transmission time a simple algorithm is proposed to generate all d t mps and the system reliability can then be computed in terms of d t mps moreover the optimal pair of minimal paths with highest system reliability could be obtained

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

about strongly polynomial time algorithms for quadratic optimization over submodular constraints we present new strongly polynomial algorithms for special cases of convex separable quadratic minimization over submodular constraints the main results are an o nm log n 2 m algorithm for the problemnetwork defined on a network onm arcs andn nodes an o n logn algorithm for thetree problem onn variables an o n logn algorithm for thenested problem and a linear time algorithm for thegeneralized upper bound problem these algorithms are the best known so far for these problems the status of the general problem and open questions are presented as well

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

sending perishable information coding improves delay constrained throughput even for single unicast this paper considers network communications under a hard timeliness constraint where a source node streams perishable information to a destination node over a directed acyclic graph subject to a hard delay constraint transmission along any edge incurs unit delay and it is required that every information bit generated at the source at the beginning of time t to be received and recovered by the destination at the end of time t mathrm d 1 where mathrm d 0 is the maximum allowed end to end delay we study the corresponding delay constrained unicast capacity problem this paper presents the first example showing that network coding nc can achieve strictly higher delay constrained throughput than routing even for the single unicast setting and the nc gain can be arbitrarily close to 2 in some instances this is in sharp contrast to the delay unconstrained mathrm d infty single unicast case where the classic min cut max flow theorem implies that coding cannot improve throughput over routing motivated by the above findings a series of investigation on the delay constrained capacity problem is also made including 1 an equivalent multiple unicast representation based on a time expanded graph approach 2 a new delay constrained capacity upper bound and its connections to the existing routing based results ying et al 2011 3 an example showing that the penalty of using random linear nc can be unbounded and 4 a counter example of the tree packing edmonds theorem in the new delay constrained setting built upon the time expanded graph approach we also discuss how our results can be readily extended to cyclic networks overall our results suggest that delay constrained communication is fundamentally different from the well understood delay unconstrained one and call for investigation participation

a global local affinity graph for image segmentation construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph cut based image segmentation methods in this paper we propose a novel sparse global local affinity graph over superpixels of an input image to capture both short and long range grouping cues and thereby enabling perceptual grouping laws including proximity similarity continuity and to enter in action through a suitable graph cut algorithm moreover we also evaluate three major visual features namely color texture and shape for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics which suggest combining these visual features with different emphases for perceptual grouping in particular an input image is first oversegmented into superpixels at different scales we postulate a gravitation law based on empirical observations and divide superpixels adaptively into small medium and large sized sets global grouping is achieved using medium sized superpixels through a sparse representation of superpixels features by solving a ell 0 minimization problem and thereby enabling continuity or propagation of local smoothness over long range connections small and large sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space and thus implementing perceptual laws for example similarity and proximity finally a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales extensive experiments are carried out on the berkeley segmentation database in comparison with several state of the art graph constructions the results show the effectiveness of the proposed approach which outperforms state of the art graphs using four different objective criteria namely the probabilistic rand index the variation of information the global consistency error and the boundary displacement error

a polynomial time algorithm for rayleigh ratio on discrete variables replacing spectral techniques for expander ratio normalized cut and cheeger constant a general form of minimizing the rayleigh ratio on discrete variables is shown here for the first time to be polynomial time solvable this is significant because major problems in clustering partitioning and imaging can be presented as the rayleigh ratio minimization on discrete variables and an orthogonality constraint these challenging problems are modeled as the normalized cut problem the graph expander ratio problem the cheeger constant problem or the conductance problem all of which are np hard these problems have traditionally been solved heuristically using the spectral technique a unified framework is provided here whereby all these problems are formulated as a constrained minimization form of a quadratic ratio referred to here as the rayleigh ratio the quadratic ratio is to be minimized on discrete variables and a single sum constraint that we call the balance or orthogonality constraint when the discreteness constraints on the variables are disregarded the resulting continuous relaxation is solved by the spectral method it is shown here that the rayleigh ratio minimization subject to the discreteness constraints requiring each variable to assume one of two values in b 1 is solvable in strongly polynomial time equivalent to a single minimum s t cut algorithm on a graph of same size as the input graph for any nonnegative value of b this discrete form for the rayleigh ratio problem was often assumed to be np hard not only is it shown here that the discrete rayleigh ratio problem is polynomial time solvable but also the algorithm is more efficient than the spectral algorithm furthermore an experimental study demonstrates that the new algorithm provides in practice an improvement often dramatic on the quality of the results of the spectral method both in terms of approximating the true optimum of the rayleigh ratio problem on both the discrete variables and the balance constraint and in terms of the subjective partition quality a further contribution here is the introduction of a problem the quantity normalized cut generalizing all the rayleigh ratio problems the discrete version of that problem is also solved with the efficient algorithm presented this problem is shown in a companion paper to enable the modeling of features essential to clustering that are valuable in practical applications

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

a fast algorithm for computing minimum 3 way and 4 way cuts for an edge weighted graph g with n vertices and m edges we present a new deterministic algorithm for computing a minimum k way cut for k 3 4 the algorithm runs in o n k 1 f n m o mn k log n 2 m time and o n 2 space for k 3 4 where f n m denotes the time bound required to solve the maximum flow problem in g the bound for k 3 matches the current best deterministic bound o mn 3 for weighted graphs but improves the bound o mn 3 to o n 2 f n m o min mn 8 3 m 3 2 n 2 for unweighted graphs the bound o mn 4 for k 4 improves the previous best randomized bound o n 6 for m o n 2 the algorithm is then generalized to the problem of finding a minimum 3 way cut in a symmetric submodular system

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

system reliability for quickest path problems under time threshold and budget many studies on hardware framework and routing policy are devoted to reducing the transmission time for a computer network the quickest path problem thus arises to find a path which sends a given amount of data from the source to the sink such that the transmission time is minimized more specifically the capacity of each arc in the network is assumed to be deterministic however in many real life networks such as computer systems telecommunication systems etc the capacity of each arc is stochastic due to failure maintenance etc such a network is named stochastic flow network hence the minimum transmission time is not a fixed number we extend the quickest path problem to evaluating the probability that d units of data can be sent from the source to the sink under both time threshold t and budget b such a probability is named system reliability a simple algorithm is proposed to generate all lower boundary points for d t b and the system reliability can then be computed in terms of such points

parametric maximum flow algorithms for fast total variation minimization this report studies the global minimization of anisotropically discretized total variation tv energies with an l p in particular l 1 and l 2 fidelity term using parametric maximum flow algorithms to minimize s t cut representations of these energies the tv l 2 model also known as the rudin osher fatemi rof model is suitable for restoring images contaminated by gaussian noise while the tv l 1 model is able to remove impulsive noise from grayscale images and perform multiscale decompositions of them preliminary numerical results on large scale two dimensional ct and three dimensional brain mr images are presented to illustrate the effectiveness of these approaches

aggregation of monotone reciprocal relations with application to group decision making this paper is composed of two complementary parts the first part is a formal investigation into the interplay of properties of reciprocal relations how monotonicity relates to some natural and intuitive properties including stochastic transitivity the goal is to aggregate monotone reciprocal relations on a given set of alternatives monotonicity is expressed w r t a linear order on the set of alternatives the second part is a practical protocol to both determine the best fitting linear order underlying the alternatives and construct a reciprocal relation monotone w r t it we formulate the problem as an optimization problem where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations we show that if stochastic monotonicity conditions are satisfied a monotone reciprocal relation is easily found on the basis of the possibly constructed stochastically monotone reciprocal distributional relation

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result