An improved bound on the one-sided minimum crossing number in two-layered drawings

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Abstract

Given a bipartite graph G = (V,W,E), a two-layered drawing consists of placing nodes in the first node set V on a straight line L1 and placing nodes in the second node set W on a parallel line L2. The one-sided crossing minimization problem asks one to find an ordering of nodes in V to be placed on L1 so that the number of arc crossings is minimized. In this paper we use a 1.4664-approximation algorithm for this problem. This improves the previously best bound 3 due to P. Eades and N. C. Wormald [Edge crossing in drawing bipartite graphs, Algorithmica 11 (1994), 379-403]. © 2005 Springer Science+Business Media, Inc.

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Nagamochi, H. (2005). An improved bound on the one-sided minimum crossing number in two-layered drawings. Discrete and Computational Geometry, 33(4), 565–591. https://doi.org/10.1007/s00454-005-1168-0

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