Variants of the mixed postman problem solvable using linear programming

Given a connected mixed graph with costs on its edges and arcs, the mixed postman problem consists of finding a minimum cost closed tour of the mixed graph traversing all of its edges and arcs. It is well-known that this problem is NP-hard. However, under certain conditions, the problem can be solve...

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Main Authors: Zaragoza Martínez, Francisco Javier, López Bracho, Rafael
Format: Artículo
Language: Inglés
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/1334
http://hdl.handle.net/10669/13018
Summary: Given a connected mixed graph with costs on its edges and arcs, the mixed postman problem consists of finding a minimum cost closed tour of the mixed graph traversing all of its edges and arcs. It is well-known that this problem is NP-hard. However, under certain conditions, the problem can be solved in polynomial time using linear programming, in other words, the corresponding polyhedra are integral. Some of these conditions are: the mixed graph is series parallel or the mixed graph is even. Also, we show that if we add the constraint that each edge is traversed exactly once then the problem can be solved in polynomial time if the set of arcs forms a forest.Keywords: Mixed graph, postman problem, linear programming.Mathematics Subject Classification: 05C45, 90C35.