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Author Chimani, Markus ♦ Gutwenger, Carsten ♦ Mutzel, Petra
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2009
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data
Subject Keyword Column generation ♦ Crossing minimization heuristics ♦ Crossing number
Abstract The crossing number of a graph $\textit{G}$ is the smallest number of edge crossings in any drawing of $\textit{G}$ into the plane. Recently, the first branch-and-cut approach for solving the crossing number problem has been presented in Buchheim et al. [2005]. Its major drawback was the huge number of variables out of which only very few were actually used in the optimal solution. This restricted the algorithm to rather small graphs with low crossing number. In this article, we discuss two column generation schemes; the first is based on traditional algebraic pricing, and the second uses combinatorial arguments to decide whether and which variables need to be added. The main focus of this article is the experimental comparison between the original approach and these two schemes. In addition, we evaluate the quality achieved by the best-known crossing number heuristic by comparing the new results with the results of the heuristic.
ISSN 10846654
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2010-01-05
Publisher Place New York
e-ISSN 10846654
Journal Journal of Experimental Algorithmics (JEA)
Volume Number 14
Page Count 15
Starting Page 3.4
Ending Page 3.18


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Source: ACM Digital Library