Stable allocations and partially ordered sets

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-11-01 DOI:10.1016/j.disopt.2022.100731

Ioannis Mourtos, Michalis Samaris

引用次数: 1

Abstract

We provide a linear description of the unconstrained stable allocations problem by proving that the corresponding polytope is affinely congruent to the order polytope of a partially ordered set. The same holds for stable matchings hence simplifying the derivation of known polyhedral results. We also show that this congruence no longer holds for the constrained version of stable allocations. As side outcomes, we characterise the neighbouring vertices of the order polytope and the partially ordered set associated with stable allocations.

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稳定分配和部分有序集

通过证明相应的多面体与偏序集的序多面体仿射全等，给出了无约束稳定分配问题的一个线性描述。这同样适用于稳定匹配，从而简化了已知多面体结果的推导。我们也证明了这个同余不再适用于稳定分配的约束版本。作为副结果，我们描述了有序多面体的邻近顶点和与稳定分配相关的部分有序集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.