Approximation algorithms for forests augmentation ensuring two disjoint paths of bounded length

Authors:
Victor Chepoi;Bertrand Estellon;Yann Vaxès
Affiliations:
LIF-Laboratoire dInformatique Fondamentale de Marseille, UMR 6166, Faculté des Sciences de Luminy, Université de la Méditerranée, F-13288 Marseille Cedex 9, France;LIF-Laboratoire dInformatique Fondamentale de Marseille, UMR 6166, Faculté des Sciences de Luminy, Université de la Méditerranée, F-13288 Marseille Cedex 9, France;LIF-Laboratoire dInformatique Fondamentale de Marseille, UMR 6166, Faculté des Sciences de Luminy, Université de la Méditerranée, F-13288 Marseille Cedex 9, France
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

Given a forest F=(V,E) and a positive integer D, we consider the problem of finding a minimum number of new edges E^' such that in the augmented graph H=(V,E@?E^') any pair of vertices can be connected by two vertex-disjoint paths of length @?D. We show that this problem and some of its variants are NP-hard, and we present approximation algorithms with worst-case bounds 6 and 4. These algorithms can be implemented in O(|V|log|V|) time.