A 2log2(n)-Approximation Algorithm for Directed Tour Cover

Authors:
Viet Hung Nguyen
Affiliations:
LIP6, Université Pierre et Marie Curie Paris 6, Paris, France and LIF, Université de la Mediterrannée, Marseille, France
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

Given a directed graph G with non-negative cost on the arcs, a directed tour cover T of G is a cycle (not necessary simple) in G such that either head or tail (or both of them) of every arc in G is touched by T . The minimum directed tour cover problem (DToCP) which is to find a directed tour cover of minimum cost, is NP -hard. It is thus interesting to design approximation algorithms with performance guarantee to solve this problem. Although its undirected counterpart (ToCP) has been studied in recent years [1,6], in our knowledge, the DTCP remains widely open. In this paper, we give a 2log2 (n )-approximation algorithm for the DTCP.