Graph orientations optimizing the number of light or heavy vertices

Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirotaka Ono

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

3 Citations (Scopus)

Abstract

This paper introduces four graph orientation problems named Maximize W -Light, Minimize W -Light, Maximize W -Heavy, and Minimize W -Heavy, where W can be any fixed non-negative integer. In each of these problems, the input is an undirected graph G and the objective is to assign a direction to each edge in G so that the number of vertices with outdegree at most W or at least W in the resulting directed graph is maximized or minimized. We derive a number of results on the computational complexity and polynomial-time approximability of these problems for different values of W and various special classes of graphs. In particular, we show that Maximize 0-Light and Minimize 1-Heavy are equivalent to Maximum Independent Set and Minimum Vertex Cover, respectively, so by allowing the value of W to vary, we obtain a new, natural generalization of the two latter problems.

Original languageEnglish
Title of host publicationCombinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers
Pages332-343
Number of pages12
Volume7422 LNCS
DOIs
Publication statusPublished - Aug 27 2012
Event2nd International Symposium on Combinatorial Optimization, ISCO 2012 - Athens, Greece
Duration: Apr 19 2012Apr 21 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7422 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Symposium on Combinatorial Optimization, ISCO 2012
CountryGreece
CityAthens
Period4/19/124/21/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Asahiro, Y., Jansson, J., Miyano, E., & Ono, H. (2012). Graph orientations optimizing the number of light or heavy vertices. In Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers (Vol. 7422 LNCS, pp. 332-343). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7422 LNCS). https://doi.org/10.1007/978-3-642-32147-4_30