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检索条件"任意字段=7th International Conference on Integer Programming and Combinatorial Optimization, IPCO 1999"

共 85 条记录，以下是31-40 订阅

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Tight Lower Bounds for Block-Structured integer Programs 25th

Tight Lower Bounds for Block-Structured Integer Programs

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25th international conference on integer programming and combinatorial optimization (ipco)

作者： Hunkenschroder, Christoph Klein, Kim-Manuel Koutecky, Martin Lassota, Alexandra Levin, Asaf TU Berlin Inst Math Formerly Berlin Germany Univ Lubeck Inst Theoret Comp Sci Lubeck Germany Charles Univ Prague Comp Sci Inst Prague Czech Republic Eindhoven Univ Technol Eindhoven Netherlands Technion Fac Data & Decis Sci Haifa Israel

ISBN: (纸本)9783031598340;9783031598357

We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern;and transposing their constraint matrix yields multi-stage IPs. the state-of-the-art algorithms to solve these IPs have an exponential gap in their running times, making it natural to ask whether this gap is inherent. We answer this question affirmative. Assuming the Exponential Time Hypothesis, we prove lower bounds showing that the exponential difference is necessary, and that the known algorithms are near optimal. Moreover, we prove unconditional lower bounds on the norms of the Graver basis, a fundamental building block of all known algorithms to solve these IPs. this shows that none of the current approaches can be improved beyond this bound.

关键词： integer programming n-fold tree-fold multi-stage (unconditional) lower bounds Eth subset sum

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Adaptivity Gaps in Two-Sided Assortment optimization 25th

Adaptivity Gaps in Two-Sided Assortment Optimization

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25th international conference on integer programming and combinatorial optimization (ipco)

作者： El Housni, Omar Torrico, Alfredo Hennebelle, Ulyssee Cornell Univ Cornell Tech New York NY 10021 USA Cornell Univ CDSES Ithaca NY USA Ecole Polytech Palaiseau France

ISBN: (纸本)9783031598340;9783031598357

We study a two-sided assortment optimization framework to address the challenge of choice congestion faced by matching platforms. the goal is to decide the assortments to offer to agents in order to maximize the expected number of matches. We identify several classes of policies that the platforms can use in their design. Our main goal is to measure the value that one class of policies have over another one. For this, we define the adaptivity gap as the worst-case ratio between the optimal value achieved by two different policy classes. First, we show that the adaptivity gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly 1 - 1/e. Second, we show that the adaptivity gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly 1/2. Finally, we observe that the worst policies are those who simultaneously show assortments to all the agents, in fact, we show that the adaptivity gap with respect to one-sided policies can be arbitrarily small. these results showcase the benefit of each class of policies and, in particular, demonstrate that the optimal value of the best class of adaptive policies is a constant multiplicative factor away from those of one-sided policies.

关键词： Matching markets Assortment optimization Adaptivity gap

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Online combinatorial Assignment in Independence Systems 25th

Online Combinatorial Assignment in Independence Systems

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25th international conference on integer programming and combinatorial optimization (ipco)

作者： Marinkovic, Javier Soto, Jose A. Verdugo, Victor Univ Chile Dept Math Engn Santiago Chile Univ Chile Ctr Math Modeling IRL CNRS 2807 Santiago Chile Pontificia Univ Catalica Chile Inst Math & Computat Engn Santiago Chile Pontificia Univ Catalica Chile Dept Ind & Syst Engn Santiago Chile

ISBN: (纸本)9783031598340;9783031598357

We consider an online multi-weighted generalization of several classic online optimization problems called the online combinatorial assignment problem. We are given an independence system over a ground set of elements and agents that arrive online one by one. Upon arrival, each agent reveals a weight function over the elements of the ground set. If the independence system is given by the matchings of a hypergraph, we recover the combinatorial auction problem, where every node represents an item to be sold, and every edge represents a bundle of items. For combinatorial auctions, Kesselheim et al. showed upper bounds of O(log log(k)/ log(k)) and O(log log(n)/ log(n)) on the competitiveness of any online algorithm, even in the random order model, where k is the maximum bundle size and n is the number of items. We provide an exponential improvement by giving upper bounds of O(log(k)/k), and O(log(n)/root n) for the prophet IID setting. Furthermore, using linear programming, we provide new and improved guarantees for the k-bounded online combinatorial auction problem (i.e., bundles of size at most k). We show a (1-e(-k))/k-competitive algorithm in the prophet IID model, a 1/(k + 1)-competitive algorithm in the prophet-secretary model using a single sample per agent, and a k(-k/(k-1))-competitive algorithm in the secretary model. Our algorithms run in polynomial time and work in more general independence systems where the offline combinatorial assignment problem admits the existence of a polynomial-time randomized algorithm that we call certificate sampler. these systems include some classes of matroids, matroid intersections, and matchoids.

关键词： Online Algorithms Linear programming combinatorial Auctions

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Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube 1

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7th international conference on integer programming and combinatorial optimization, ipco 1999

作者： Eisenbrand, Friedrich Schulz, Andreas S. Max-Planck-Institut für Informatik Im Stadtwald SaarbrückenD-66123 Germany MIT Sloan School of Management and Operations Research Center E53-361 CambridgeMA02139 United States

ISBN: (数字)9783540487777

ISBN: (纸本)3540660194

Gomory’s and Chvátal’s cutting-plane procedure proves recursively the validity of linear inequalities for the integer hull of a given polyhedron. the number of rounds needed to obtain all valid inequalities is known as the Chv´ atal rank of the polyhedron. It is well-known that the Chv´ atal rank can be arbitrarily large, even if the polyhedron is bounded, if it is of dimension 2, and if its integer hull is a 0/1-polytope. We prove that the Chvátal rank of polyhedra featured in common relaxations of many combinatorial optimization problems is rather small;in fact, the rank of any polytope contained in the n-dimensional 0/1-cube is at most 3n2lg n. this improves upon a recent result of Bockmayr et al. [6] who obtained an upper bound of O(n3 lgn). Moreover, we refine this result by showing that the rank of any polytope in the 0/1-cube that is defined by inequalities with small coefficients is O(n). the latter observation explains why for most cutting planes derived in polyhedral studies of several popular combinatorial optimization problems only linear growth has been observed (see, e.g., [13]);the coefficients of the corresponding inequalities are usually small. Similar results were only known for monotone polyhedra before. Finally, we provide a family of polytopes contained in the 0/1-cube the Chvátal rank of which is at least (1 + Ε)nfor some Ε > 0;the best known lower bound was n. © Springer-Verlag Berlin Heidelberg 1999.

关键词： combinatorial optimization

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Separating k-MEDIAN from the Supplier Version 25th

Separating k-MEDIAN from the Supplier Version

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25th international conference on integer programming and combinatorial optimization (ipco)

作者： Anand, Aditya Lee, Euiwoong Univ Michigan Ann Arbor MI 48109 USA

ISBN: (纸本)9783031598340;9783031598357

Given a metric space (V, d) along with an integer k, the k-Median problem asks to open k centers C subset of V to minimize Sigma(v is an element of V) d(v, C), where d(v, C) := mi(n is an element of C) d(v, c). While the best-known approximation ratio 2.613 holds for the more general supplier version where an additional set F subset of V is given with the restriction C subset of F, the best known hardness for these two versions are 1+1/e approximate to 1.36 and 1+2/e approximate to 1.73 respectively, using the same reduction from Maximum k-Coverage. We prove the following two results separating them. 1. We give a 1.546-parameterized approximation algorithm that runs in time f(k)n(O(1)). Since 1+ 2/e is proved to be the optimal approximation ratio for the supplier version in the parameterized setting, this result separates the original k-Median from the supplier version. 2. We prove a 1.416-hardness for polynomial-time algorithms assuming the Unique Games Conjecture. this is achieved via a new finegrained hardness of Maximum k-Coverage for small set sizes. Our upper bound and lower bound are derived from almost the same expression, with the only difference coming from the well-known separation between the powers of LP and SDP on (hypergraph) vertex cover.

关键词： Approximation algorithms Clustering Parameterized approximation optimization Hardness of approximation

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A Better-than-1.6-Approximation for Prize-Collecting TSP 25th

A Better-Than-1.6-Approximation for Prize-Collecting TSP

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25th international conference on integer programming and combinatorial optimization (ipco)

作者： Blauth, Jannis Klein, Nathan Nagele, Martin Univ Bonn Res Inst Discrete Math Bonn Germany Univ Bonn Hausdorff Ctr Math Bonn Germany Inst Adv Study Olden Lane Princeton NJ 08540 USA

ISBN: (纸本)9783031598340;9783031598357

Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. the quality of a solution is then measured by adding the length of the tour and the sum of all penalties of vertices that are not visited. We present a polynomial-time approximation algorithm with an approximation guarantee slightly below 1.6, where the guarantee is with respect to the natural linear programming relaxation of the problem. this improves upon the previous best-known approximation ratio of 1.774. Our approach is based on a known decomposition for solutions of this linear relaxation into rooted trees. Our algorithm takes a tree from this decomposition and then performs a pruning step before doing parity correction on the remainder. Using a simple analysis, we bound the approximation guarantee of the proposed algorithm by (1 + root 5)/2 approximate to 1.618, the golden ratio. With some additional technical care we further improve it to 1.599.

关键词： combinatorial optimization Approxim. Algorithms TSP

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Automated Configuration of Mixed integer programming Solvers

Automated Configuration of Mixed Integer Programming Solvers

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7th international conference Integration of AI and OR Techniques in Constraint programming for combinatorial optimization Problems

作者： Hutter, Frank Hoos, Holger H. Leyton-Brown, Kevin Univ British Columbia Vancouver BC V6T 1Z4 Canada

ISBN: (纸本)9783642135194

State-of-the-art solvers for mixed integer programming (MIP) problems are highly parameterized, and finding parameter settings that achieve high performance for specific types of MIP instances is challenging. We study the application of an automated algorithm configuration procedure to different MIP solvers, instance types and optimization objectives. We show that this fully-automated process yields substantial improvements to the performance of three MIP solvers: CPLEX, GUROBI, and LPSOLVE. Although our method can be used "out of the box" without any domain knowledge specific to MIP, we show that it outperforms the CPLEX special-purpose automated tuning tool.

关键词： integer programming

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Parity constrained κ-Edge-connected orientations 7th

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7th international conference on integer programming and combinatorial optimization, ipco 1999

作者： Frank, András Király, Zoltán Department of Operations Research Eötvös University Rákóczi út 5 BudapestH-1088 Hungary Ericsson Traffic Laboratory Laborc u. 1 BudapestH-1037 Hungary Department of Computer Science Eötvös University Rákóczi út 5 BudapestH-1088 Hungary

ISBN: (纸本)3540660194

Parity (matching theory) and connectivity (network flows) are two main branches of combinatorial optimization. In an attempt to understand better their interrelation, we study a problem where both parity and connectivity requirements are imposed. the main result is a characterization of undirected graphs G = (V, E) having a κ-edge-connected T-odd orientation for every subset T ⊆ V with |E| + |T| even. (T-odd orientation: the in-degree of v is odd precisely if v is in T.) As a corollary, we obtain that every (2κ + 2)-edge-connected graph with |V| + |E| even has a κ-edge-connected orientation in which the in-degree of every node is odd. Along the way, a structural characterization will be given for digraphs with a root-node s having κ + 1 edge-disjoint paths from s to every node and κ edge-disjoint paths from every node to s. © Springer-Verlag Berlin Heidelberg 1999.

关键词： combinatorial optimization

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Valid inequalities for problems with additive variable upper bounds 1

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7th international conference on integer programming and combinatorial optimization, ipco 1999

作者： Atamtürk, Alper Nemhauser, George L. Savelsbergh, Martin W. P. Department of Industrial Engineering and Operations Research University of California BerkeleyCA94720-1777 United States School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332-0205 United States

ISBN: (数字)9783540487777

ISBN: (纸本)3540660194

We study the facial structure of a polyhedron associated with the single node relaxation of network flow problems with additive variable upper bounds. this type of structure arises, for example, in network design/expansion problems and in production planning problems with setup times. We first derive two classes of valid inequalities for this polyhedron and give the conditions under which they are facet-defining. then we generalize our results through sequence independent lifting of valid inequalities for lower-dimensional projections. Our computational experience with large network expansion problems indicates that these inequalities are very effective in improving the quality of the linear programming relaxations. © Springer-Verlag Berlin Heidelberg 1999.

关键词： Linear programming

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Optimal 3-Terminal cuts and linear programming 1

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7th international conference on integer programming and combinatorial optimization, ipco 1999

作者： Cunningham, William H. Tang, Lawrence Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada Department of Mathematics University of British Columbia VancouverBCV6T 1Y8 Canada

ISBN: (数字)9783540487777

ISBN: (纸本)3540660194

Given an undirected graph G = (V, E) and three specified terminal nodes t1, t2, t3, a 3-cutis a subset A of Esuch that no two terminals are in the same component of G\A. If a non-negative edge weight ce is specified for each e ∈ E, the optimal 3-cut problemis to find a 3-cut of minimum total weight. this problem is NP-hard, and in fact, is max-SNP-hard. An approximation algorithm having performance guarantee has recently been given by Călinescu, Karloff, and Rabani. It is based on a certain linear programming relaxation, for which it is shown that the optimal 3-cut has weight at most times the optimal LP value. It is proved here that can be improved to, and that this is best possible. As a consequence, we obtain an approximation algorithm for the optimal 3-cut problem having performance guarantee 12/11. © Springer-Verlag Berlin Heidelberg 1999.

关键词： Approximation algorithms

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