Graph orientations optimizing the number of light or heavy vertices

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

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

3 Citations (Scopus)


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
Number of pages12
Publication statusPublished - 27 Aug 2012
Externally publishedYes
Event2nd International Symposium on Combinatorial Optimization, ISCO 2012 - Athens, Greece
Duration: 19 Apr 201221 Apr 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


Conference2nd International Symposium on Combinatorial Optimization, ISCO 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


Dive into the research topics of 'Graph orientations optimizing the number of light or heavy vertices'. Together they form a unique fingerprint.

Cite this