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.
Original language | English (US) |
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Pages (from-to) | 747-762 |
Number of pages | 16 |
Journal | Journal of Combinatorial Optimization |
Volume | 22 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2011 |
Externally published | Yes |
Keywords
- Adjacency matrix
- Crossing minimization
- Network flow
- TSP
ASJC Scopus subject areas
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics