Graph orientation algorithms to minimize the maximum outdegree

Yuichi Asahiro, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be AP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, min{w max/wmin, (2 - ε)}-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.

Original languageEnglish
Pages (from-to)197-215
Number of pages19
JournalInternational Journal of Foundations of Computer Science
Volume18
Issue number2
DOIs
Publication statusPublished - Apr 1 2007

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All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

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