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

Approximating the Minimum Tour Cover of a Digraph

Received: 2 March 2011; in revised form: 24 March 2011 / Accepted: 2 April 2011 / Published: 20 April 2011
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
PDF Full-text Download PDF Full-Text [179 KB, uploaded 20 April 2011 10:48 CEST]

Export to BibTeX |

MDPI and ACS Style

Nguyen, V.H. Approximating the Minimum Tour Cover of a Digraph. Algorithms 2011, 4, 75-86.

AMA Style

Nguyen VH. Approximating the Minimum Tour Cover of a Digraph. Algorithms. 2011; 4(2):75-86.

Chicago/Turabian Style

Nguyen, Viet Hung. 2011. "Approximating the Minimum Tour Cover of a Digraph." Algorithms 4, no. 2: 75-86.

Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert