A rearrangement of adjacency matrix based approach for solving the crossing minimization problem

Neng Fan () and Panos M. Pardalos ()
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Neng Fan: University of Florida
Panos M. Pardalos: University of Florida

Journal of Combinatorial Optimization, 2011, vol. 22, issue 4, No 19, 747-762

Abstract: Abstract In this paper, we first present a binary linear programming formulation for the crossing minimization problem (CMP) in bipartite graphs. Then we use the models of a modified minimum cost flow problem (MMCF) and a travelling salesman problem (TSP) to approximatively solve the CMP by rearranging the adjacency matrix of the bipartite graph. Our approaches are useful for problems defined on dense bipartite graphs. In addition, we compute the exact crossing numbers for some general dense graphs.

Keywords: Crossing minimization; Adjacency matrix; Network flow; TSP (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-010-9326-6

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