{"title":"Stable allocations and partially ordered sets","authors":"Ioannis Mourtos, Michalis Samaris","doi":"10.1016/j.disopt.2022.100731","DOIUrl":null,"url":null,"abstract":"<div><p><span>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 </span>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.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"46 ","pages":"Article 100731"},"PeriodicalIF":0.9000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528622000378","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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