An approximation algorithm for the two-layered graph drawing problem

Authors:
Atsuko Yamaguchi;Akihiro Sugimoto
Affiliations:
Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama, Japan;Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama, Japan
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

We present a polynomial-time approximation algorithm for the minimum edge crossings problem for two-layered graphs. We show the relationship between the approximation ratio of our algorithm and the maximum degree of the vertices in the lower layer of the input graph. When the maximum degree is not greater than four, the approximation ratio is two and this ratio monotonically increases to three as the maximum degree becomes larger. We also present our experiments, showing that our algorithm constructs better solutions than the barycenter method and the median method for dense graphs as well as sparse graphs.