the proceedings contain 33 papers. the special focus in this conference is on integerprogramming and combinatorialoptimization. the topics include: A Better-than-1.6-Approximation for Prize-Collecting TSP;on Ma...
ISBN:
(纸本)9783031598340
the proceedings contain 33 papers. the special focus in this conference is on integerprogramming and combinatorialoptimization. the topics include: A Better-than-1.6-Approximation for Prize-Collecting TSP;on Matrices over a Polynomial Ring with Restricted Subdeterminants;a First Order Method for Linear programming Parameterized by Circuit Imbalance;approximately Packing Dijoins via Nowhere-Zero Flows;capacitated Facility Location with Outliers and Uniform Facility Costs;integer Points in Arbitrary Convex Cones: the Case of the PSD and SOC Cones;the Extension Complexity of Polytopes with Bounded Integral Slack Matrices;assortment optimization with Visibility Constraints;adaptivity Gaps in Two-Sided Assortment optimization;two-Stage Stochastic Stable Matching;von Neumann-Morgenstern Stability and Internal Closedness in Matching theory;fully-Dynamic Load Balancing;pairwise-Independent Contention Resolution;An FPTAS for Connectivity Interdiction;tight Lower Bounds for Block-Structured integer Programs;A Lower Bound for the Max Entropy Algorithm for TSP;on the Number of Degenerate Simplex Pivots;on the Partial Convexification of the Low-Rank Spectral optimization: Rank Bounds and Algorithms;on the Congruency-Constrained Matroid Base;online combinatorial Assignment in Independence Systems;decomposing Probability Marginals Beyond Affine Requirements;polynomial Algorithms to Minimize 2/3-Submodular Functions;A 43-Approximation for the Maximum Leaf Spanning Arborescence Problem in DAGs;extending the Primal-Dual 2-Approximation Algorithm Beyond Uncrossable Set Families;network Flow Problems with Electric Vehicles;lower Bounds on the Complexity of Mixed-integer Programs for Stable Set and Knapsack;relaxation Strength for Multilinear optimization: McCormick Strikes Back;online Algorithms for Spectral Hypergraph Sparsification;fast combinatorial Algorithms for Efficient Sortation;a New Branching Rule for Range Minimization Problems;sensitivity Analysis for Mixed Binary Quadrat
With developments in artificial intelligence, computer science, and network technologies, modern confrontational scenarios are increasingly related to multi-agent systems characterized by multi-network. To reduce the ...
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We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick lineari...
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ISBN:
(纸本)9783031598340;9783031598357
We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick linearization (Operations Research Letters 51 (2023) 146-152). In this paper we extend the result to more general linearizations, and present a simpler proof. Moreover, we complement Khajavirad's result by showing that the intersection of the relaxations of such linearizations and the extended flower relaxation are equally strong.
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral con...
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ISBN:
(纸本)9783031598340;9783031598357
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbert bases, under the action of a finitely generated group. We also extend notions of total dual integrality, Gomory-Chv ' atal closure, and Carath ' eodory rank to integer points in arbitrary cones.
Consider a matroid where all elements are labeled with an element in Z. We are interested in finding a base where the sum of the labels is congruent to g (mod m). We show that this problem can be solved in (O) over ti...
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ISBN:
(纸本)9783031598340;9783031598357
Consider a matroid where all elements are labeled with an element in Z. We are interested in finding a base where the sum of the labels is congruent to g (mod m). We show that this problem can be solved in (O) over tilde (2(4m)nr(5/6)) time for a matroid with n elements and rank r, when m is either the product of two primes or a prime power. the algorithm can be generalized to all moduli and, in fact, to all abelian groups if a classic additive combinatorics conjecture by Schrijver and Seymour holds true. We also discuss the optimization version of the problem.
We obtain new transference bounds that connect two active areas of research: proximity and sparsity of solutions to integer programs. Specifically, we study the additive integrality gap of the integer linear programs ...
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ISBN:
(纸本)9783031598340;9783031598357
We obtain new transference bounds that connect two active areas of research: proximity and sparsity of solutions to integer programs. Specifically, we study the additive integrality gap of the integer linear programs min{c.x : x is an element of P boolean AND Z(n)}, where P = {x is an element of R-n : Ax = b, x >= 0} is a polyhedron in the standard form determined by an integer m x n matrix A and an integer vector b. the main result of the paper gives an upper bound for the integrality gap that drops exponentially in the size of support of the optimal solutions corresponding to the vertices of the integer hull of P. Additionally, we obtain a new proximity bound that estimates the l(2)-distance from a vertex of P to its nearest integer point in the polyhedron P. the proofs make use of the results from the geometry of numbers and convex geometry.
the simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to ...
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ISBN:
(纸本)9783031598340;9783031598357
the simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better extreme point along an improving edge-direction of the underlying polyhedron. A key issue in the simplex algorithm's performance is degeneracy, which may lead to a (potentially long) sequence of basis exchanges which do not change the current extreme point solution. In this paper, we prove that it is always possible to limit the number of consecutive degenerate pivots that the simplex algorithm performs to n - m - 1, where n is the number of variables and m is the number of equality constraints of a given LP in standard equality form.
One of the most famous conjectures in combinatorialoptimization is the four-thirds conjecture, which states that the integrality gap of the subtour LP relaxation of the TSP is equal to 4/3. For 40 years, the best kno...
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ISBN:
(纸本)9783031598340;9783031598357
One of the most famous conjectures in combinatorialoptimization is the four-thirds conjecture, which states that the integrality gap of the subtour LP relaxation of the TSP is equal to 4/3. For 40 years, the best known upper bound was 1.5, due to Wolsey [Wol80]. Recently, Karlin, Klein, and Oveis Gharan [KKO22] showed that the max entropy algorithm for the TSP gives an improved bound of 1.5 - 10(-36). In this paper, we show that the approximation ratio of the max entropy algorithm is at least 1.375, even for graphic TSP. thus the max entropy algorithm does not appear to be the algorithm that will ultimately resolve the four-thirds conjecture in the affirmative, should that be possible.
Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate ...
ISBN:
(纸本)9783031598340;9783031598357
Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in a typical hub-and-spoke fashion. In practice, such consolidation requires parcel sortation. In this work, we propose a mathematical model for the physical requirements, and limitations of parcel sortation. We then show that it is NP-hard to determine whether a feasible sortation plan exists. We discuss several settings, where (near-) feasibility of a given sortation instance can be determined efficiently. the algorithms we propose are fast and build on combinatorial witness set type lower bounds that are reminiscent and extend those used in earlier work on degree-bounded spanning trees and arborescences.
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