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Algorithms 2011, 4(2), 75-86; doi:10.3390/a4020075
Article

Approximating the Minimum Tour Cover of a Digraph

Received: 2 March 2011 / Revised: 24 March 2011 / Accepted: 2 April 2011 / Published: 20 April 2011
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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 necessarily 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, in our knowledge, the DToCP remains widely open. In this paper, we give a 2 log2(n)-approximation algorithm for the DToCP.
Keywords: approximation algorithm; graph algorithm; packing and covering; tour cover; tree cover approximation algorithm; graph algorithm; packing and covering; tour cover; tree cover
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Nguyen, V.H. Approximating the Minimum Tour Cover of a Digraph. Algorithms 2011, 4, 75-86.

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