An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings

Authors:
Hiroshi Nagamochi
Affiliations:
Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Discrete & Computational Geometry
Year:
2005

Citing 0
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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].