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

Fingerprint

Directed graphs
Diamonds
Hardness

All Science Journal Classification (ASJC) codes

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

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).

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 proceedingConference 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.
Asahiro Y, Miyano E, Ono H. 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. 2008. (Conferences in Research and Practice in Information Technology Series).
Asahiro, Yuichi ; Miyano, Eiji ; Ono, Hirotaka. / Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree. 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).
@inproceedings{12f69098967d4606a15a0e6272a0cae5,
title = "Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree",
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.",
author = "Yuichi Asahiro and Eiji Miyano and Hirotaka Ono",
year = "2008",
month = "12",
day = "1",
language = "English",
isbn = "9781920682583",
series = "Conferences in Research and Practice in Information Technology Series",
booktitle = "Theory of Computing 2008 - Proceedings of the Fourteenth Computing",

}

TY - GEN

T1 - Graph classes and the complexity of the graph orientation minimizing the maximum weighted outdegree

AU - Asahiro, Yuichi

AU - Miyano, Eiji

AU - Ono, Hirotaka

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863591626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863591626&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84863591626

SN - 9781920682583

T3 - Conferences in Research and Practice in Information Technology Series

BT - Theory of Computing 2008 - Proceedings of the Fourteenth Computing

ER -