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

Authors:
Neng Fan;Panos M. Pardalos
Affiliations:
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA;Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA
Venue:
Journal of Combinatorial Optimization
Year:
2011

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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.