Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree

Yuichi Asahiro, Eiji Miyano, Hirotaka Ono

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

3 Citations (Scopus)

Abstract

Given an undirected graph with edge weights, we are asked to find an orientation, i.e., an assignment of a direction to each edge, so as to minimize the weighted maximum outdegree in the resulted directed graph. The problem is called MMO, and is a restricted variant of the well-known minimum makespan problem. As previous studies, it is shown that MMO is in P for trees, weak NP-hard for planar bipartite graphs, and strong NP-hard for general graphs. There are still gaps between those graph classes. The objective of this paper is to show tight thresholds of complexity: We show that MMO is (i) in P for cactuses, (ii) weakly NP-hard for outerplanar graphs, and also (iii) strongly NP-hard for P4-bipartite graphs. The latter two are minimal superclasses of the former. Also, we show the NP-hardness for the other related graph classes, diamond-free, house-free, series-parallel, bipartite and planar.

Original languageEnglish
Title of host publicationTheory of Computing 2008 - Proceedings of the Fourteenth Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2008
Publication statusPublished - Dec 1 2008
EventTheory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008 - Wollongong, NSW, Australia
Duration: Jan 22 2008Jan 25 2008

Publication series

NameConferences in Research and Practice in Information Technology Series
Volume77
ISSN (Print)1445-1336

Other

OtherTheory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008
CountryAustralia
CityWollongong, NSW
Period1/22/081/25/08

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Information Systems
  • Software

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  • Cite this

    Asahiro, Y., Miyano, E., & Ono, H. (2008). Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree. In Theory of Computing 2008 - Proceedings of the Fourteenth Computing: The Australasian Theory Symposium, CATS 2008 (Conferences in Research and Practice in Information Technology Series; Vol. 77).