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

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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

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

Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers. Vol. 7422 LNCS 2012. p. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7422 LNCS).

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

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, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7422 LNCS, pp. 332-343, 2nd International Symposium on Combinatorial Optimization, ISCO 2012, Athens, Greece, 4/19/12. https://doi.org/10.1007/978-3-642-32147-4_30
Asahiro Y, Jansson J, Miyano E, Ono H. Graph orientations optimizing the number of light or heavy vertices. In Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers. Vol. 7422 LNCS. 2012. p. 332-343. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-32147-4_30
Asahiro, Yuichi ; Jansson, Jesper ; Miyano, Eiji ; Ono, Hirotaka. / Graph orientations optimizing the number of light or heavy vertices. Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers. Vol. 7422 LNCS 2012. pp. 332-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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