Graph orientations optimizing the number of light or heavy vertices

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 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 problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every 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. 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 are derived. In particular, it is shown that MAXIMIZE 0-LIGHT and MINIMIZE 1-HEAVY are identical to MAXIMUM INDEPENDENT SET and MINIMUM VERTEX COVER, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.
Original languageEnglish
Pages (from-to)441-465
Number of pages25
JournalJournal of Graph Algorithms and Applications
Issue number1
Publication statusPublished - 1 Aug 2015
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics


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