Crossing minimization in weighted bipartite graphs

Given a bipartite graph G=(L0,L1,E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and...

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Bibliographic Details
Published inJournal of discrete algorithms (Amsterdam, Netherlands) Vol. 7; no. 4; pp. 439 - 452
Main Authors Çakıroḡlu, Olca A., Erten, Cesim, Karataş, Ömer, Sözdinler, Melih
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2009
Subjects
Approximation algorithms
Combinatorial optimization
Crossing minimization
Weighted bipartite graphs
Weighted bipartite graphs
Crossing minimization
Approximation algorithms
Combinatorial optimization
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Summary:Given a bipartite graph G=(L0,L1,E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and polynomial-time algorithms with a constant approximation ratio have been suggested. We generalize the problem and consider the version where the edges have nonnegative weights. Although this problem is more general and finds specific applications in automatic graph layout problems similar to those of the unweighted case, it has not received as much attention. We provide a new technique that efficiently approximates a solution to this more general problem within a constant approximation ratio of 3. In addition we provide appropriate generalizations of some common heuristics usually employed for the unweighted case and compare their performances.
ISSN:1570-8667
1570-8675
DOI:10.1016/j.jda.2008.08.003