On the -median polytope and the directed odd cycle inequalities: Triangle-free oriented graphs

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• 作者：Mourad Baï ; ou^a ; ^{baiou@isima.fr" class="auth_mail" title="E-mail the corresponding author} ; Francisco Barahona^b ; ^{barahon@us.ibm.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：pp-median problem ; Uncapacitated facility location problem ; Odd cycle inequalities
• 刊名：Discrete Optimization
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：22
• 期：part_PA
• 页码：206-224
• 全文大小：709 K

文摘

We study the effect of the odd directed cycle inequalities in the description of the polytope associated with the p$p$-median problem. We treat oriented graphs, i.e., if (u,v)$(u,v)$ is in the arc-set, then (v,u)$(v,u)$ is not in the arc-set. We characterize the oriented graphs for which the obvious linear relaxation together with the directed odd cycle inequalities describe the p$p$-median polytope. This study has two parts: in this paper we treat triangle-free graphs, then in a second paper we use induction on the number of triangles to treat general oriented graphs.