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 |
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All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Computer Science Applications
- Hardware and Architecture
- Information Systems
- Software
Cite this
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
}
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.
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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 -