Approximation algorithms for the graph orientation minimizing the maximum weighted outdegree

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

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

10 Citations (Scopus)


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
Number of pages11
Publication statusPublished - 1 Dec 2007
Externally publishedYes
Event3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States
Duration: 6 Jun 20078 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4508 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
Country/TerritoryUnited States
CityPortland, OR

ASJC Scopus subject areas

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

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