A new exact algorithm for the two-sided crossing minimization problem

Authors:
Lanbo Zheng;Christoph Buchheim
Affiliations:
School of Information Technologies, University of Sydney, Australia and IMAGEN program, National ICT Australia;Computer Science Department, University of Cologne, Germany
Venue:
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Year:
2007

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Abstract

The Two-Sided Crossing Minimization (TSCM) problem calls for minimizing the number of edge crossings of a bipartite graph where the two sets of vertices are drawn on two parallel layers and edges are drawn as straight lines. This well-known problem has important applications in VLSI design and automatic graph drawing. In this paper, we present a new branch-and-cut algorithm for the TSCM problem by modeling it directly to a binary quadratic programming problem. We show that a large number of effective cutting planes can be derived based on a reformulation of the TSCM problem. We compare our algorithm with a previous exact algorithm by testing both implementations with the same set of instances. Experimental evaluation demonstrates the effectiveness of our approach.