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

Neng Fan, Panos M. Pardalos

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)747-762
Number of pages16
JournalJournal of Combinatorial Optimization
Volume22
Issue number4
DOIs
StatePublished - 2011
Externally publishedYes

Fingerprint

Crossing Minimization
Adjacency Matrix
Rearrangement
Bipartite Graph
Minimization Problem
Traveling salesman problem
Linear programming
Minimum Cost Flow
Crossing number
Travelling salesman problems
Binary
Costs
Formulation
Graph in graph theory
Model

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

Cite this

A rearrangement of adjacency matrix based approach for solving the crossing minimization problem. / Fan, Neng; Pardalos, Panos M.

In: Journal of Combinatorial Optimization, Vol. 22, No. 4, 2011, p. 747-762.

Research output: Contribution to journalArticle

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