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

N1 - Funding Information:
An extended abstract of this article was presented in Proceedings of Fourteenth Computing: The Australasian Theory Symposium (CATS 2008), Wollongong, NSW, Australia, January 22–25, 2008 (Asahiro et al. (2008) [2] ). This work is partially supported by KAKENHI (Nos. 16092222 , 16092223 , 17700022 , 18700014 , 18700015 , 20500017 and 22700019 ).
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

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

T2 - Theory of Computing 2008 - 14th Computing: The Australasian Theory Symposium, CATS 2008

Y2 - 22 January 2008 through 25 January 2008

ER -