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

Yuichi Asahiro; Eiji Miyano; Hirotaka Ono

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

Yuichi Asahiro, Eiji Miyano, Hirotaka Ono

mathematics and information

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Theory of Computing 2008 - Proceedings of the Fourteenth Computing
Subtitle of host publication	The Australasian Theory Symposium, CATS 2008
Publication status	Published - Dec 1 2008
Event	Theory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008 - Wollongong, NSW, Australia Duration: Jan 22 2008 → Jan 25 2008

Publication series

Name	Conferences in Research and Practice in Information Technology Series
Volume	77
ISSN (Print)	1445-1336

Other

Other	Theory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008
Country	Australia
City	Wollongong, NSW
Period	1/22/08 → 1/25/08

All Science Journal Classification (ASJC) codes

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

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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).

Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree. / Asahiro, Yuichi; Miyano, Eiji; Ono, Hirotaka.

Theory of Computing 2008 - Proceedings of the Fourteenth Computing: The Australasian Theory Symposium, CATS 2008. 2008. (Conferences in Research and Practice in Information Technology Series; Vol. 77).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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, Theory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008, Wollongong, NSW, Australia, 1/22/08.

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