Graph orientations optimizing the number of light or heavy vertices

Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirotaka Ono

Research output: Contribution to journalArticle

4 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 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
Volume19
Issue number1
DOIs
Publication statusPublished - Aug 1 2015

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Graph in graph theory
Maximise
Directed graphs
Approximability
Computational complexity
Undirected Graph
Polynomials
Directed Graph
Assign
Polynomial time
Computational Complexity
Non-negative
Vary
Minimise
Integer
Vertex of a graph
Class
Generalization

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

Graph orientations optimizing the number of light or heavy vertices. / Asahiro, Yuichi; Jansson, Jesper; Miyano, Eiji; Ono, Hirotaka.

In: Journal of Graph Algorithms and Applications, Vol. 19, No. 1, 01.08.2015, p. 441-465.

Research output: Contribution to journalArticle

Asahiro, Yuichi ; Jansson, Jesper ; Miyano, Eiji ; Ono, Hirotaka. / Graph orientations optimizing the number of light or heavy vertices. In: Journal of Graph Algorithms and Applications. 2015 ; Vol. 19, No. 1. pp. 441-465.
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