Approximating the Minimum Tour Cover of a Digraph

Given a directed graph G with non-negative cost on the arcs, a directed tour cover T ofG is a cycle (not necessarily simple) inG 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, in our knowledge, the DToCP remains widely open. In this paper, we give a 2 log2(n)-approximation algorithm for the DToCP.