k-Level Crossing Minimization Is NP-Hard for Trees
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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.
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- 1.Albacea, E.: A Linear Algorithm for Bipartite Drawing with Minimum Edge Crossings of Complete Binary Trees. Philippine Computing Journal 1(1), 1–5 (2006)Google Scholar
- 4.Demestrescu, C., Finocchi, I.: Breaking Cycles for Minimizing Crossings. Journal of Experimental Algorithmics 6(2) (2001)Google Scholar