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.
This work was partially supported by the Marie Curie Research Training Network 504438 (ADONET) funded by the European Commission.
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Zheng, L., Buchheim, C. (2007). A New Exact Algorithm for the Two-Sided Crossing Minimization Problem. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_32
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DOI: https://doi.org/10.1007/978-3-540-73556-4_32
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