严格Δ-modular图形多面体锥的整数壳的扩展公式

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-12-19 DOI:10.1016/j.orl.2024.107235

Joseph Paat , Zach Walsh , Luze Xu

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引用次数: 0

摘要

Conforti等人给出了一类双模约束整数规划的紧凑扩展公式，即对无不相交奇环图的稳定集多面体进行建模。我们扩展了他们的技术，为平移多面体锥的整数壳设计了紧凑的扩展公式，其约束矩阵严格为Δ-modular，并且具有表示图形矩阵的行。我们的工作推广了Conforti等关于奇环截数至少为4的4连通图的重要特例。我们还讨论了这些假设的必要性。

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Extended formulations for the integer hull of strictly Δ-modular cographic polyhedral cones

Conforti et al. give a compact extended formulation for a class of bimodular-constrained integer programs, namely those that model the stable set polytope of a graph with no disjoint odd cycles. We extend their techniques to design compact extended formulations for the integer hull of translated polyhedral cones whose constraint matrix is strictly Δ-modular and has rows that represent a cographic matroid. Our work generalizes the important special case from Conforti et al. concerning 4-connected graphs with odd cycle transversal number at least 4. We also discuss the necessity of our assumptions.

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.