通过二值化降低 Chvátal 等级

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

Operations Research Letters Pub Date : 2024-05-01 DOI:10.1016/j.orl.2024.107119

Gérard Cornuéjols, Vrishabh Patil

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引用次数: 0

摘要

在一篇经典论文中，Chvátal 介绍了一种加强整数程序多面体松弛 P 的舍入过程；递归应用时，获得 P 中整数解凸壳所需的迭代次数称为 Chvátal 秩。我们给出了 P 的紧凑扩展表述，通过引入二进制变量进行描述，其秩为 L 的多项式。

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Reducing the Chvátal rank through binarization

In a classical paper, Chvátal introduced a rounding procedure for strengthening the polyhedral relaxation P of an integer program; applied recursively, the number of iterations needed to obtain the convex hull of the integer solutions in P is known as the Chvátal rank. Chvátal showed that this rank can be exponential in the input size L needed to describe P. We give a compact extended formulation of P, described by introducing binary variables, whose rank is polynomial in L.

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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.