k-level crossing minimization is NP-hard for trees

Authors:
Martin Harrigan;Patrick Healy
Affiliations:
Complex & Adaptive Systems Laboratory, University College Dublin, Ireland;Dept. of Computer Science & Information Systems, University of Limerick, Ireland
Venue:
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Year:
2011

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Abstract

The k-level crossing minimization problem for graphs has received much interest in the graph drawing literature. In this paper we focus on the special case of trees. We show that the 2-level crossing minimization problem for trees where the order of the vertices on one level is fixed is solvable in quadratic time. We also show that the k-level crossing minimization problem for trees for an arbitrary number of levels is NP-Hard. This result exposes a source of difficulty for algorithm designers that compounds earlier results relating to the 2-level crossing minimization problem for graphs.