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

Authors:
Victor Chepoi;Bertrand Estellon;Yann Vaxès
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la, Méditerranée, Marseille, France;Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la, Méditerranée, Marseille, France;Laboratoire d'Informatique Fondamentale de Marseille, Faculté des Sciences de Luminy, Universitée de la, Méditerranée, Marseille, France
Venue:
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Year:
2005

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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.