Francisco Javier Zaragoza Martínez - The Windy Postman Problem on Series-Parallel Graphs

dmtcs:3396 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3396
The Windy Postman Problem on Series-Parallel GraphsArticle

Authors: Francisco Javier Zaragoza Martínez 1

  • 1 Departamento de Sistemas [Azcapotzalco]

The windy postman problem is the NP-hard problem of finding the minimum cost of a tour traversing all edges of an undirected graph, where the cost of traversal of an edge depends on the direction. Given an undirected graph $G$, we consider the polyhedron $O(G)$ induced by the linear programming relaxation of a well-known integer programming formulation of the problem. We say that $G$ is windy postman perfect if $O(G)$ is integral. There exists a polynomial-time algorithm, based on the ellipsoid method, to solve the windy postman problem for the class of windy postman perfect graphs. Eulerian graphs and trees are windy postman perfect. By considering a family of polyhedra related to $O(G)$, we prove that series-parallel graphs are windy postman perfect, therefore solving a conjecture of [Win1987a].


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: windy postman problem,series-parallel graphs,integral polyhedra,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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