budgeted matching and budgeted matroid intersection via the gasoline puzzle many polynomial time solvable combinatorial optimization problems become np hard if an additional complicating constraint is added to restrict the set of feasible solutions in this paper we consider two such problems namely maximum weight matching and maximum weight matroid intersection with one additional budget constraint we present the first polynomial time approximation schemes for these problems similarly to other approaches for related problems our schemes compute two solutions to the lagrangian relaxation of the problem and patch them together to obtain a near optimal solution however due to the richer combinatorial structure of the problems considered here standard patching techniques do not apply to circumvent this problem we crucially exploit the adjacency relations on the solution polytope and surprisingly the solution to an old combinatorial puzzle

a simple lp relaxation for the asymmetric traveling salesman problem it is a long standing open question in combinatorial optimization whether the integrality gap of the subtour linear program relaxation subtour lp for the asymmetric traveling salesman problem atsp is a constant the study on the structure of this linear program is important and extensive in this paper we give a new and simpler lp relaxation for the atsp our linear program consists of a single type of constraints that combine both the subtour elimination and the degree constraints in the traditional subtour lp as a result we obtain a much simpler relaxation in particular it is shown that the extreme solutions of our program have at most 2n 2 non zero variables improving the bound 3n 2 proved by vempala and yannakakis for the ones obtained by the subtour lp nevertheless the integrality gap of the new linear program is larger than that of the traditional subtour lp by at most a constant factor

discrete signal matching using coarse to fine wavelet basis functions in this paper we propose a matching algorithm to estimate accurate and dense displacements between two signals the displacements are characterized by a coarse to fine wavelet representation which is a linear combination of hierarchical basis functions developed by cai and wang siam numer anal 33 3 1996 937 the coarser scale basis function has larger support while the finer scale basis function has smaller support during the iterative minimization process the basis functions are utilized as large to small windows in selecting global to local regions for signal matching the estimated wavelet coefficients are then used to reconstruct the signal in a coarse to fine manner two sets of synthetic examples one with small displacement and the other with large displacements have been employed to illustrate the advantages of the wavelet based method this method has been applied to estimate the dense disparity between stereo images in several real examples and the results demonstrate its effectiveness

gotta efficiently catch them all pokemon go meets orienteering problems abstract in this paper a new routing problem referred to as the generalized clustered orienteering problem gcop is studied the problem is motivated by the mobile phone game pokemon go an augmented reality game for mobile devices holding a record breaking reception within the first month of its release more than 100 million users have installed the game on their devices the game s immense popularity has spawned several side businesses including taxi tours visiting locations where the game can be played as well as companies offering to play the game for users during times when they cannot further applications arise in typical operative transportation problems that seek for tours that are both time effective and profitable besides the typical traveling distances in the gcop we also have prizes or revenues associated with the nodes additionally we are given with k node subsets clusters and a budget b for the length of the tour the optimization task is to find a tour that maximizes the total collected prize while ensuring that i at least one node of each cluster is visited and ii the total distance of the tour does not exceed the budget b in order to solve the gcop to optimality a polynomial sized mixed integer linear programming mip formulation and an exponential sized mip formulation are presented while the first formulation is tackled by a state of the art branch and bound bb moreover the proposed b c is further enhanced with valid inequalities a lifting procedure for strengthening inequalities as well as initialization and primal heuristics the computational performance of the proposed approaches is assessed in an extensive computational study using real world instances that combine crowd sourced data associated with the pokemon go game with street maps of three european cities as well as instances derived from the tsplib testbed the obtained results show that the b c approach i largely outperforms the b b algorithm and that ii it is very effective for providing optimal or nearly optimal solutions within reasonable running times for both sets of instances

approximating minimum bounded degree spanning trees to within one of optimal in the minimum bounded degree spanning tree problem we are given an undirected graph g v e with a degree upper bound bv on each vertex v v and the task is to find a spanning tree of minimum cost that satisfies all the degree bounds let opt be the cost of an optimal solution to this problem in this article we present a polynomial time algorithm which returns a spanning tree t of cost at most opt and dt v bv 1 for all v where dt v denotes the degree of v in t this generalizes a result of furer and raghavachari 1994 to weighted graphs and settles a conjecture of goemans 2006 affirmatively the algorithm generalizes when each vertex v has a degree lower bound av and a degree upper bound bv and returns a spanning tree with cost at most opt and av 1 dt v bv 1 for all v v this is essentially the best possible the main technique used is an extension of the iterative rounding method introduced by jain 2001 for the design of approximation algorithms

on line generalized steiner problem the generalized steiner problem gsp is defined as follows we are given a graph with non negative edge weights and a set of pairs of vertices the algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path off line gsp approximation algorithms were given in agarwal et al siam j comput 24 3 1995 440 and goemans and williamson siam j comput 24 2 1995 296 we consider the on line gsp in which pairs of vertices arrive on line and are needed to be connected immediately we show that the online min cost i e greedy strategy for this problem has o log2 n competitive ratio the previous best algorithm was o nlog n competitive workshop on algorithms and data structures 1993 pp 622 633 following this work a different non greedy algorithm has been shown to achieve an o log n competitive ratio proceedings of the 29th acm symposium on theory of computing 1997 pp 344 353 we also consider the network connectivity leasing problem which is a generalization of the gsp here edges of the graph can be either bought or leased for different costs we provide simple randomized algorithm based on on line generalized steiner algorithms whose competitive ratio is within a constant factor of the best competitive algorithm for the on line gsp

a hierarchical symmetric stereo algorithm using dynamic programming in this paper a new hierarchical stereo algorithm is presented the algorithm matches individual pixels in corresponding scanlines by minimizing a cost function several cost functions are compared the algorithm achieves a tremendous gain in speed and memory requirements by implementing it hierarchically the images are downsampled an optimal number of times and the disparity map of a lower level is used as offset disparity map at a higher level an important contribution consists of the complexity analysis of the algorithm it is shown that this complexity is independent of the disparityrange this result is also used to determine the optimal number of downsample levels this speed gain results in the ability to use more complex compute intensive cost functions that deliver high quality disparity maps another advantage of this algorithm is that cost functions can be chosen independent of the optimisation algorithm the algorithm in this paper is symmetric i e exactly the same matches are found if left and right image are swapped finally the algorithm was carefully implemented so that a minimal amount of memory is used it has proven its efficiency on large images with a high disparity range as well as its quality examples are given in this paper

a locally adaptive window for signal matching this article presents a signal matching algorithm that can select an appropriate window size adaptively so as to obtain both precise and stable estimation of correspondences matching two signals by calculating the sum of squared differences ssd over a certain window is a basic technique in computer vision given the signals and a window there are two factors that determine the difficulty of obtaining precise matching the first is the variation of the signal within the window which must be large enough relative to noise that the ssd values exhibit a clear and sharp minimum at the correct disparity the second factor is the variation of disparity within the window which must be small enough that signals of corresponding positions are duly compared these two factors present conflicting requirements to the size of the matching window since a larger window tends to increase the signal variation but at the same time tends to include points of different disparity a window size must be adaptively selected depending on local variations of signal and disparity in order to compute a most certain estimate of disparity at each point there has been little work on a systematic method for automatic window size selection the major difficulty is that while the signal variation is measurable from the input the disparity variation is not since disparities are what we wish to calculate we introduce here a statistical model of disparity variation within a window and employ it to establish a link between the window size and the uncertainty of the computed disparity this allows us to choose the window size that minimizes uncertainty in the disparity computed at each point this article presents a theory for the model and the resultant algorithm together with analytical and experimental results that demonstrate their effectiveness

quota traveling car renter problem the quota traveling car renter problem is the quota variant of the traveling car renter problem a graph is given where a bonus is associated with each vertex the bonus is collected at every visited vertex several cars are available to travel the edges of the graph each of which associates weights with the edges the problem involves finding a cycle on a subset of vertices such that a predefined minimum sum of bonuses is obtained at least the objective is to minimize the cost of the tour using the available cars in this study we propose an integer programming model for the problem which is solved and we present optimal solutions for 24 instances we propose an evolutionary algorithm with a plasmid operator which we compare with a memetic algorithm we also present the results obtained based on computational experiments with 72 instances

complexity and approximation for traveling salesman problems with profits in tsp with profits we have to find an optimal tour and a set of customers satisfying a specific constraint in this paper we analyze three different variants of tsp with profits that are np hard in general we study their computational complexity on special structures of the underlying graph both in the case with and without service times to the customers we present polynomial algorithms for the polynomially solvable cases and fully polynomial time approximation schemes fptas for some np hard cases

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

piecemeal graph exploration by a mobile robot we study how a mobile robot can learn an unknown environment in a piecemeal manner the robot s goal is to learn a complete map of its environment while satisfying the constraint that it must return every so often to its starting position for refueling say the environment is modeled as an arbitrary undirected graph which is initially unknown to the robot we assume that the robot can distinguish vertices and edges that it has already explored we present a surprisingly efficient algorithm for piecemeal learning an unknown undirected graph g v e in which the robot explores every vertex and edge in the graph by traversing at most o e v1 o 1 edges this nearly linear algorithm improves on the best previous algorithm in which the robot traverses at most o e v2 edges we also give an application of piecemeal learning to the problem of searching a graph for a treasure

fuzzy genetic algorithm and applications abstract in this paper we introduce fuzzy genetic algorithms to approximately solve fuzzy optimization problems we argue that this technique can produce good approximate solutions by applying it to solve a fuzzy optimization problem other applications of fuzzy genetic algorithms to fuzzy optimization the fuzzy maximum flow problem fuzzy regression and tuning a fuzzy controller are also presented

evolution program for deterministic and stochastic optimizations abstract this paper presents an evolution program for deterministic and stochastic optimizations to overcome premature convergence and stalling of the solution we suggest an exponential fitness scaling scheme to avoid the chromosomes jamming into a corner we introduce mutation 1 which mutates the chromosomes in a free direction to improve the chromosomes we introduce mutation 2 which mutates the chromosomes in the gradient direction or its negative according to the kind of problem monte carlo simulation will be employed to solve the multiple integral which is the most difficult task in the stochastic optimization finally some numerical examples are discussed

a unified algorithm for degree bounded survivable network design we present an approximation algorithm for the minimum bounded degree steiner network problem that returns a steiner network of cost at most two times the optimal and the degree on each vertex v v is at most min b v 3r mathrm max 2b v 2 min bv 3rmax 2bv 2 where r mathrm max rmax is the maximum connectivity requirement and b v bv is the given degree bound on v v this unifies simplifies and improves the previous results for this problem

physical search problems with probabilistic knowledge this paper considers the problem of an agent or a team of agents searching for a resource or tangible good in a physical environment where the resource or good may possibly be obtained at one of several locations the cost of acquiring the resource or good at a given location is uncertain a priori and the agents can observe the true cost only when physically arriving at this location sample applications include agents in exploration and patrol missions e g an agent seeking to find the best location to deploy sensing equipment along its path the uniqueness of these settings is in that the cost of observing a new location is determined by distance from the current one impacting the consideration for the optimal search order although this model captures many real world scenarios it has not been investigated so far we analyze three variants of the problem differing in their objective minimizing the total expected cost maximizing the success probability given an initial budget and minimizing the budget necessary to obtain a given success probability for each variant we first introduce and analyze the problem with a single agent either providing a polynomial solution to the problem or proving it is np complete we also introduce a fully polynomial time approximation scheme algorithm for the minimum budget variant in the multi agent case we analyze two models for managing resources shared and private budget models we present polynomial algorithms that work for any fixed number of agents in the shared or private budget model for non communicating agents in the private budget model we present a polynomial algorithm that is suitable for any number of agents we also analyze the difference between homogeneous and heterogeneous agents both with respect to their allotted resources and with respect to their capabilities finally we define our problem in an environment with self interested agents we show how to find a nash equilibrium in polynomial time and prove that the bound on the performance of our algorithms with respect to the social welfare is tight

optimal deterministic algorithms for some variants of online quota traveling salesman problem abstract this paper is concerned with the online quota traveling salesman problem depending on the symmetry of the metric and the requirement for the salesman to return to the origin four variants are analyzed we present optimal deterministic algorithms for each variant defined on a general space a real line or a half line as a byproduct an improved lower bound for a variant of online tsp on a half line is also obtained

ordinal measures for image correspondence we present ordinal measures of association for image correspondence in the context of stereo linear correspondence measures like correlation and the sum of squared difference between intensity distributions are known to be fragile ordinal measures which are based on relative ordering of intensity values in windows rank permutations have demonstrable robustness by using distance metrics between two rank permutations ordinal measures are defined these measures are independent of absolute intensity scale and invariant to monotone transformations of intensity values like gamma variation between images we have developed simple algorithms for their efficient implementation experiments suggest the superiority of ordinal measures over existing techniques under nonideal conditions these measures serve as a general tool for image matching that are applicable to other vision problems such as motion estimation and texture based image retrieval

a matter of degree improved approximation algorithms for degree bounded minimum spanning trees in this paper we present a new bicriteria approximation algorithm for the degree bounded minimum spanning tree problem in this problem we are given an undirected graph a nonnegative cost function on the edges and a positive integer b and the goal is to find a minimum cost spanning tree t with maximum degree at most b in an n node graph our algorithm finds a spanning tree with maximum degree o b logn and cost o optb where optb is the minimum cost of any spanning tree whose maximum degree is at most b our algorithm uses ideas from lagrangean duality we show how a set of optimum lagrangean multipliers yields bounds on both the degree and the cost of the computed solution

dependent chance programming a class of stochastic optimization this paper provides a theoretical framework of dependent chance programming as well as dependent chance multiobjective programming and dependent chance goal programming which are new types of stochastic optimization a stochastic simulation based genetic algorithm is also designed for solving dependent chance programming models

motion estimation with quadtree splines this paper presents a motion estimation algorithm based on a new multiresolution representation the quadtree spline this representation describes the motion field as a collection of smoothly connected patches of varying size where the patch size is automatically adapted to the complexity of the underlying motion the topology of the patches is determined by a quadtree data structure and both split and merge techniques are developed for estimating this spatial subdivision the quadtree spline is implemented using another novel representation the adaptive hierarchical basis spline and combines the advantages of adaptively sized correlation windows with the speedups obtained with hierarchical basis preconditioners results are presented on some standard motion sequences

on the problem of possibilistic optimization abstract this paper is a continuation on the author s investigation on possibilistic optimization problems which are considered from general methodological positions of possibility theory and managing uncertainty as well to tackle optimization tasks under uncertainty a calculus for possibilities is developed leading to classic and interval valued optimization

primal dual meets local search approximating msts with nonuniform degree bounds we present a new bicriteria approximation algorithm for the degree bounded minimum cost spanning tree mst problem given an undirected graph with nonnegative edge weights and a degree bound b find a spanning tree of maximum node degree b and minimum total edge cost our algorithm outputs a tree of maximum degree at most a constant times b and total edge cost at most a constant times that of a minimum cost degree b bounded spanning tree while our new algorithm is based on ideas from lagrangian relaxation as is our previous work siam j comput 31 2002 pp 1783 1793 it does not rely on computing a solution to a linear program instead it uses a repeated application of kruskal s mst algorithm interleaved with a combinatorial update of approximate lagrangian node multipliers maintained by the algorithm these updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times leading to overall progress and a proof of the performance guarantee a second useful feature of our algorithm is that it can handle nonuniform degree bounds on the nodes given distinct bounds bv for every node v in v the output tree has degree at most o bv log v for every v in v as before the cost of the tree is at most a constant times that of a minimum cost tree obeying all degree bounds

improved approximation algorithms for maximum lifetime problems in wireless networks a wireless ad hoc network consists of a collection of transceivers positioned in the plane each transceiver is equipped with a limited battery charge the battery charge is reduced after each transmission depending on the transmission distance one of the major problems in wireless network design is to route network traffic efficiently so as to maximize the network lifetime i e the number of successful transmission rounds in this paper we consider rooted maximum lifetime broadcast convergecast problems in wireless settings the instance consists of a directed graph g v e with edge weight w e the power needed to transmit a message along e for every email protected e node capacity b v the battery charge of v for every email protected v and a root r the goal is to find a maximum size collection t 1 t k of broadcast convergecast trees rooted at r such that i 1 kw d t i v b v where d t v is the set of edges leaving v in t in the single topology version the same tree is used to transmit all the messages namely all the broadcast convergecast trees t i are identical using recent work on degree constrained network design problems nutov 2008 26 we give constant ratio approximation algorithms for various broadcast and convergecast problems improving the previously best known approximation w 1 email protected by elkin et al 2011 12 similar results are shown for the more general rooted maximum lifetime mixedcast problem where in addition we are given an integer c 0 and the goal is to find the maximum integer k so that k broadcast and ck convergecast rounds can be performed we also consider the model with partial level aggregation

spacetime stereo a unifying framework for depth from triangulation depth from triangulation has traditionally been investigated in a number of independent threads of research with methods such as stereo laser scanning and coded structured light considered separately we propose a common framework called spacetime stereo that unifies and generalizes many of these previous methods to show the practical utility of the framework we develop two new algorithms for depth estimation depth from unstructured illumination change and depth estimation in dynamic scenes based on our analysis we show that methods derived from the spacetime stereo framework can be used to recover depth in situations in which existing methods perform poorly

fuzzy programming with fuzzy decisions and fuzzy simulation based genetic algorithm this paper provides a spectrum of chance constrained programming as well as chance constrained multiobjective programming and chance constrained goal programming with fuzzy rather than crisp decisions which will seek a fuzzy set from the given reference collection as an optimal solution the technique of fuzzy simulation is also presented to check fuzzy chance constraints and to handle fuzzy objective and goal constraints finally a fuzzy simulation based genetic algorithm for solving these models will be designed and illustrated by some numerical examples

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

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

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

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

deeper local search for parameterized and approximation algorithms for maximum internal spanning tree the maximum internal spanning tree problem asks for a spanning tree of a given graph that has the maximum number of internal vertices among all spanning trees of this graph in its parameterized version we are interested in whether the graph has a spanning tree with at least k internal vertices fomin et al 2013 4 crafted a very ingenious reduction rule and showed that a simple application of this rule is sufficient to yield a 3k vertex kernel implying an o 8 k time parameterized algorithm using depth 2 local search knauer and spoerhase 2015 9 developed a 5 3 approximation algorithm for the optimization version we try deeper local search we conduct a thorough combinatorial analysis on the obtained spanning trees and explore their algorithmic consequences we first observe that from the spanning tree obtained by depth 3 local search one can easily find a reducible structure and apply the reduction rule of fomin et al this gives an improved kernel of 2k vertices and as a by product a deterministic algorithm running in time o 4 k we then go even deeper by considering the spanning tree obtained by depth 5 local search it is shown that the number of internal vertices of this spanning tree is at least 2 3 of the maximum number a spanning tree can have thereby delivering an improved approximation algorithm with ratio 1 5 for the problem

multilevel enhancement and detection of stereo disparity surfaces abstract the problem of stereo vision has been of increasing interest to the computer vision community over the past decade this paper presents a new computational framework for matching a pair of stereo images arising from viewing the same object from two different positions in contrast to previous work this approach formulates the matching problem as detection of a bright coherent disparity surface in a 3d image called the spatio disparity space sds image the sds images represents the goodness of each and every possible match a nonlinear filter is proposed for enhancing the disparity surface in the sds image and for suppressing the noise this filter is used to construct a hyperpyramid representation of the sds image then the disparity surface is detected using a coarse to fine control structure the proposed method is robust to photometric and geometric distortions in the stereo images and has a number of computational advantages it produces good results for complex scenes

hardness of approximation for vertex connectivity network design problems in the survivable network design problem sndp the goal is to find a minimum cost spanning subgraph satisfying certain connectivity requirements we study the vertex connectivity variant of sndp in which the input specifies for each pair of vertices a required number of vertex disjoint paths connecting them we give the first strong lower bound on the approximability of sndp showing that the problem admits no efficient 2 log 1 epsilon n ratio approximation for any fixed epsilon 0 unless np subseteq dtime n polylog n we show hardness of approximation results for some important special cases of sndp and we exhibit the first lower bound on the approximability of the related classical np hard problem of augmenting the connectivity of a graph using edges from a given set

on generalizations of network design problems with degree bounds iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems in this paper we extend the scope of the iterative relaxation method in two directions 1 by handling more complex degree constraints in the minimum spanning tree problem namely laminar crossing spanning tree and 2 by incorporating degree bounds in other combinatorial optimization problems such as matroid intersection and lattice polyhedra we give new or improved approximation algorithms hardness results and integrality gaps for these problems our main result is a 1 b o log n approximation algorithm for the minimum crossing spanning tree mcst problem with laminar degree constraints the laminar mcst problem is a natural generalization of the well studied bounded degree mst and is a special case of general crossing spanning tree we give an additive log c m hardness of approximation for general mcst even in the absence of costs c 0 is a fixed constant and m is the number of degree constraints this also leads to a multiplicative log c m hardness of approximation for the robust k median problem anthony et al in math oper res 35 79 101 2010 improving over the previously known factor 2 hardness we then consider the crossing contra polymatroid intersection problem and obtain a 2 2b 1 approximation algorithm where is the maximum element frequency this models for example the degree bounded spanning set intersection in two matroids finally we introduce the crossing latticep olyhedron problem and obtain a 1 b 2 1 approximation algorithm under certain condition this result provides a unified framework and common generalization of various problems studied previously such as degree bounded matroids

a simple stereo algorithm to recover precise object boundaries and smooth surfaces in area based stereo matching there is a problem called boundary overreach i e the recovered object boundary turns out to be wrongly located away from the real one this is especially harmful to segmenting objects using depth information a few approaches have been proposed to solve this problem however these techniques tend to degrade on smooth surfaces that is there seems to be a trade off problem between recovering precise object edges and obtaining smooth surfaces in this paper we propose a new simple method to solve this problem using multiple stereo pairs and multiple windowing our method detects the region where the boundary overreach is likely to occur let us call it bo region and adopts appropriate methods for the bo and non bo regions although the proposed method is quite simple the experimental results have shown that it is very effective at recovering both sharp object edges at their correct locations and smooth object surfaces

new approximation guarantees for minimum weight k trees and prize collecting salesmen we consider a formalization of the following problem a salesperson must sell some quota of brushes in order to win a trip to hawaii this salesperson has a map a weighted graph in which each city has an attached demand specifying the number of brushes that can be sold in that city what is the best route to take to sell the quota while traveling the least distance possible notice that unlike the standard traveling salesman problem not only do we need to figure out the order in which to visit the cities but we must decide the more fundamental question which cities do we want to visit in this paper we give the first approximation algorithm having a polylogarithmic performance guarantee for this problem as well as for the slightly more general prize collecting traveling salesman problem pctsp of balas and a variation we call the bank robber problem also called the orienteering problem by golden levi and vohra we do this by providing an o log2 k approximation to the somewhat cleaner k mst problem which is defined as follows given an undirected graph on n nodes with nonnegative edge weights and an integer k leq n find the tree of least weight that spans k vertices if desired one may specify in the problem a root vertex that must be in the tree as well our result improves on the previous best bound of o sqrt k of ravi et al

hybrid stereo matching with a new relaxation scheme of preserving disparity discontinuity abstract a hybrid stereo matching algorithm using a combined edge and region based method is proposed to take the advantage of each technique i e an exactly matched point and a full resolution disparity map region based matching is typically more efficient than edge based matching however a region based matcher lacks the capability of generating an accurate fine resolution disparity map the generation of such a map can be better accomplished by using edge based techniques accordingly regions and edges both play important and complimentary roles in a binocular stereo process since it is crucial that an efficient and robust stereo system utilizes the most appropriate set of primitives a nonlinear laplacian filter is modified to extract proper primitives since each pixel value of a second order differentiated image includes important information for the intensity profile information such as edge signed and zero pixels obtained by the modified nonlinear laplacian filter is used to determine the matching strategy consequently the proposed matching algorithm consists of edge signed and zero or residual pixel matching different matching strategies are adopted in each matching step adaptive windows with variable sizes and shapes are also used to consider the local information of the pixels in addition a new relaxation scheme based on the statistical distribution of matched errors and constraint functions which contain disparity smoothness uniqueness and discontinuity preservation is proposed to efficiently reduce mismatched points in unfavorable conditions unlike conventional relaxation schemes the erosion in an abrupt area of a disparity map is considerably reduced because a discontinuity preservation factor based on a survival possibility function is added to the proposed relaxation the relaxation scheme can be applied to various methods such as block feature region object based matching methods and so on by modifying the excitatory set of the smoothness constraint function experimental results show that the proposed matching algorithm is effective for various images even if the image has a high content of noise and repeated patterns the convergence rate of the relaxation and the output quality are both improved

optimization models and a ga based algorithm for stochastic time cost trade off problem in real life projects both the trade off between the project cost and the project completion time and the uncertainty of the environment are considerable aspects for decision makers however the research on the time cost trade off problem seldom concerns stochastic environments besides optimizing the expected value of the objective is the exclusive decision making criterion in the existing models for the stochastic time cost trade off problem in this paper two newly developed alternative stochastic time cost trade off models are proposed in which the philosophies of chance constrained programming and dependent chance programming are adopted for decision making in addition a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi optimal schedules under different decision making criteria the goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments

dependent chance programming with fuzzy decisions dependent chance programming dcp is a new type of stochastic programming and has been extended to the area of fuzzy programming this paper provides a spectrum of dcp and dependent chance multiobjective programming dcmop as well as dependent chance goal programming dcgp models with fuzzy rather than crisp decisions the terms of uncertain environment event chance function and induced constraints are discussed in the case of fuzzy decisions a technique of fuzzy simulation is also designed for computing chance functions finally we present a fuzzy simulation based genetic algorithm for solving these models and illustrate its effectiveness by some numerical examples

extracting view dependent depth maps from a collection of images stereo correspondence algorithms typically produce a single depth map in addition to the usual problems of occlusions and textureless regions such algorithms cannot model the variation in scene or object appearance with respect to the viewing position in this paper we propose a new representation that overcomes the appearance variation problem associated with an image sequence rather than estimating a single depth map we associate a depth map with each input image or a subset of them our representation is motivated by applications such as view interpolation and depth based segmentation for model building or layer extraction we describe two approaches to extract such a representation from a sequence of images the first approach which is more classical computes the local depth map associated with each chosen reference frame independently the novelty of this approach lies in its combination of shiftable windows temporal selection and graph cut optimization the second approach simultaneously optimizes a set of self consistent depth maps at multiple key frames since multiple depth maps are estimated simultaneously visibility can be modeled explicitly and disparity consistency imposed across the different depth maps results which include a difficult specular scene example show the effectiveness of our approach

an exact e constraint method for bi objective combinatorial optimization problems application to the traveling salesman problem with profits abstract this paper describes an exact constraint method for bi objective combinatorial optimization problems with integer objective values this method tackles multi objective optimization problems by solving a series of single objective subproblems where all but one objectives are transformed into constraints we show in this paper that the pareto front of bi objective problems can be efficiently generated with the constraint method furthermore we describe heuristics based on information gathered from previous subproblems that significantly speed up the method this approach is used to find the exact pareto front of the traveling salesman problem with profits a variant of the traveling salesman problem in which a profit or prize value is associated with each vertex the goal here is to visit a subset of vertices while addressing two conflicting objectives maximize the collected prize and minimize the travel costs we report the first exact results for this problem on instances derived from classical vehicle routing and traveling salesman problem instances with up to 150 vertices results on approximations of the pareto front obtained from a variant of our exact algorithm are also reported

restricted 2 factor polytopes the optimal k restricted 2 factor problem consists of finding in a complete undirected graph k n a minimum cost 2 factor subgraph having degree 2 at every node with all components having more than k nodes the problem is a relaxation of the well known symmetric travelling salesman problem and is equivalent to it when k n 1 we study the k restricted 2 factor polytope we present a large class of valid inequalities called bipartition inequalities and describe some of their properties some of these results are new even for the travelling salesman polytope for the case k 3 the triangle free 2 factor polytope we derive a necessary and sufficient condition for such inequalities to be facet inducing

uncertain programming a unifying optimization theory in various uncertain environments by uncertain programming we mean the optimization theory in generally uncertain random fuzzy fuzzy random grey etc environments three broad classes of uncertain programming are expected value models and chance constrained programming as well as dependent chance programming in order to solve general uncertain programming models a simulation based genetic algorithm is also documented finally some applications and further research problems appearing in this area are posed

approximation algorithms for problems combining facility location and network design we present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design we first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy at bulk costs and provide a combinatorial approximation algorithm we also show that the integer programming formulation of this problem has small integrality gap we extend the model to the version when there is a bound on the number of facilities that may be opened

dynamic algorithms via the primal dual method abstract we develop a dynamic version of the primal dual method for optimization problems and apply it to obtain the following results 1 for the dynamic set cover problem we maintain an o f 2 approximately optimal solution in o f log m n amortized update time where f is the maximum frequency of an element n is the number of sets and m is the maximum number of elements in the universe at any point in time 2 for the dynamic b matching problem we maintain an o 1 approximately optimal solution in o log 3 n amortized update time where n is the number of nodes in the graph

a multiple baseline stereo a stereo matching method that uses multiple stereo pairs with various baselines generated by a lateral displacement of a camera to obtain precise distance estimates without suffering from ambiguity is presented matching is performed simply by computing the sum of squared difference ssd values the ssd functions for individual stereo pairs are represented with respect to the inverse distance and are then added to produce the sum of ssds this resulting function is called the sssd in inverse distance it is shown that the sssd in inverse distance function exhibits a unique and clear minimum at the correct matching position even when the underlying intensity patterns of the scene include ambiguities or repetitive patterns the authors first define a stereo algorithm based on the sssd in inverse distance and present a mathematical analysis to show how the algorithm can remove ambiguity and increase precision experimental results with real stereo images are presented to demonstrate the effectiveness of the algorithm

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

survivable network design with degree or order constraints we present algorithmic and hardness results for network design problems with degree or order constraints the first problem we consider is the survivable network design problem with degree constraints on vertices the objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds b v on the vertices this includes the well studied minimum bounded degree spanning tree problem as a special case our main result is a 2 2b v 3 approximation algorithm for the edge connectivity survivable network design problem with degree constraints where the cost of the returned solution is at most twice the cost of an optimum solution satisfying the degree bounds and the degree of each vertex v is at most 2b v 3 this implies the first constant factor bicriteria approximation algorithms for many degree constrained network design problems including the minimum bounded degree steiner forest problem our results also extend to directed graphs and provide the first constant factor bicriteria approximation algorithms for the minimum bounded degree arborescence problem and the minimum bounded degree strongly k edge connected subgraph problem in contrast we show that the vertex connectivity survivable network design problem with degree constraints is hard to approximate even when the cost of every edge is zero a striking aspect of our algorithmic result is its simplicity it is based on the iterative relaxation method which is an extension of jain s iterative rounding method this provides an elegant and unifying algorithmic framework for a broad range of network design problems we also study the problem of finding a minimum cost lambda edge connected subgraph with at least k vertices which we call the k lambda subgraph problem this generalizes some well studied classical problems such as the k mst and the minimum cost lambda edge connected subgraph problems we give a polylogarithmic approximation for the k 2 subgraph problem however by relating it to the densest k subgraph problem we provide evidence that the k lambda subgraph problem might be hard to approximate for arbitrary lambda

dependent chance programming in fuzzy environments dependent chance programming is a new type of stochastic programming this paper provides a framework of dependent chance programming as well as dependent chance multiobjective programming and dependent chance goal programming in fuzzy environment as opposed to stochastic environment we also extend the concepts of uncertain environments events chance functions and induced constraints from stochastic to fuzzy cases finally a fuzzy simulation based genetic algorithm is illustrated by some numerical examples of dependent chance programming models

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

stereo matching algorithm based on modified wavelet decomposition process multiresolutional representation such as pyramidal structures is useful for stereo matching as coarse to fine strategy however conventional pyramidal structures using gaussian or laplacian filters lose much information due to their low pass filtering characteristics and also cannot obtain any spatial orientation selectivity the adoption of wavelet transform can remedy these problems but at the time of image translation it changes wavelet coefficients in this paper a pyramid using modified wavelet decomposition process is proposed to have translation invariance the image transformed by the proposed method is converted into appropriate multiple features without loss of information since the importance of each feature is determined heuristically in the multiple feature based stereo matching method it is very difficult to fuse them adequately in the proposed algorithm the weight of each feature that is the relative importance of each feature is decided from the similarity between the intensities in the local region of each left and right wavelet channels since the window size used for the decision of weight and disparity values greatly influences the processed result the window is adaptively determined from the disparities estimated in the coarse resolution and low varying channel of fine resolution the window size must be large enough to obtain signal to noise ratio but not too large as to induce the effects of projective distortion also a new relaxation algorithm which can reduce false matches without blurring the disparity edge is proposed by integrating adaptive weight variable window selection method and relaxation process an accurate and stable disparity map is obtained experimental results for various images show that the proposed algorithm has good performance even if the image has the unfavorable conditions

spline based image registration the problem of image registration subsumes a number of problems and techniques in multiframe image analysis including the computation of optic flow general pixel based motion stereo correspondence structure from motion and feature tracking we present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems in particular we show how to compute local flow global parametric flow rigid flow resulting from camera egomotion and multiframe versions of the above problems using a spline based description of the flow removes the need for overlapping correlation windows and produces an explicit measure of the correlation between adjacent flow estimates we demonstrate our algorithm on multiframe image registration and the recovery of 3d projective scene geometry we also provide results on a number of standard motion sequences

multi objective vehicle routing problems routing problems such as the traveling salesman problem and the vehicle routing problem are widely studied both because of their classic academic appeal and their numerous real life applications similarly the field of multi objective optimization is attracting more and more attention notably because it offers new opportunities for defining problems this article surveys the existing research related to multi objective optimization in routing problems it examines routing problems in terms of their definitions their objectives and the multi objective algorithms proposed for solving them

an extension of the christofides heuristic for the generalized multiple depot multiple traveling salesmen problem abstract we study a generalization of the classical traveling salesman problem where multiple salesmen are positioned at different depots of which only a limited number k can be selected to service customers for this problem only two 2 approximation algorithms are available in the literature here we improve on these algorithms by showing that a non trivial extension of the well known christofides heuristic has a tight approximation ratio of 2 1 2 k in doing so we develop a body of analysis which can be used to build new approximation algorithms for other vehicle routing problems

a note on chance constrained programming with fuzzy coefficients this paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives we also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints finally a fuzzy simulation based genetic algorithm is employed to solve a numerical example

lp rounding approximation algorithms for stochastic network design we study the steiner tree problem and the single cable single sink network design problem under a two stage stochastic model with recourse and finitely many scenarios in these models some edges are purchased in a first stage when only probabilistic information about the second stage is available in the second stage one of a finite number of specified scenarios is realized which results in the set of terminals becoming known and the opportunity to purchase additional edges under an inflated cost function to augment the first stage solution we provide constant factor approximation algorithms for these problems by rounding the linear relaxation of ip formulations of the problems our algorithms involve solving the linear relaxation first followed by a primal dual routine that is guided by the lp solution we also show that because our bounds are local the cost of each component is bounded by its cost in the lp solution we are able to obtain bounds that guard against a form of downside risk

stereo matching with nonlinear diffusion one of the central problems in stereo matching and other image registration tasks is the selection of optimal window sizes for comparing image regions this paper addresses this problem with some novel algorithms based on iteratively diffusing support at different disparity hypotheses and locally controlling the amount of diffusion based on the current quality of the disparity estimate it also develops a novel bayesian estimation technique which significantly outperforms techniques based on area based matching ssd and regular diffusion we provide experimental results on both synthetic and real stereo image pairs