Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

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Variants of the mixed postman problem solvable using linear programming
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Keywords

Mixed graph
postman problem
linear programming
Gráfica mixta
problema de cartero
programación lineal

How to Cite

Zaragoza Martínez, F. J., & López Bracho, R. (2012). Variants of the mixed postman problem solvable using linear programming. Revista De Matemática: Teoría Y Aplicaciones, 19(2), 201–210. https://doi.org/10.15517/rmta.v19i2.1334

Abstract

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.

https://doi.org/10.15517/rmta.v19i2.1334
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