Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree

Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

Given an undirected graph G = (V, E) and a weight function w : E → ℤ+, we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. In this paper (1) we prove that the problem is strongly NP-hard if all edge weights belong to the set {1 ,k}, where k is any integer greater than or equal to 2, and that there exists no pseudo-polynomial time approximation algorithm for this problem whose approximation ratio is smaller than (1 + 1/k) unless P=NP; (2) we present a polynomial time algorithm that approximates the general version of the problem within a factor of (2 - 1/k), where k is the maximum weight of an edge in G; (3) we show how to approximate the special case in which all edge weights belong to {1, k} within a factor of 3/2 for k = 2 (note that this matches the inapproximability bound above), and (2 - 2/(k + 1)) for any k ≥ 3, respectively, in polynomial time.

Original languageEnglish
Title of host publicationAlgorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
Pages167-177
Number of pages11
Volume4508 LNCS
Publication statusPublished - 2007
Event3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States
Duration: Jun 6 2007Jun 8 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4508 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
CountryUnited States
CityPortland, OR
Period6/6/076/8/07

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

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    Asahiro, Y., Jansson, J., Miyano, E., Ono, H., & Zenmyo, K. (2007). Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree. In Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings (Vol. 4508 LNCS, pp. 167-177). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4508 LNCS).