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Approximating the Minimum Tour Cover of a Digraph
LIP6, Universite Pierre et Marie Curie Paris 6, 4 place Jussieu, Paris, France
Received: 2 March 2011; in revised form: 24 March 2011 / Accepted: 2 April 2011 / Published: 20 April 2011
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
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Cite This Article
MDPI and ACS Style
Nguyen, V.H. Approximating the Minimum Tour Cover of a Digraph. Algorithms 2011, 4, 75-86.
Nguyen VH. Approximating the Minimum Tour Cover of a Digraph. Algorithms. 2011; 4(2):75-86.
Nguyen, Viet Hung. 2011. "Approximating the Minimum Tour Cover of a Digraph." Algorithms 4, no. 2: 75-86.