## An Improved Approximation to the One-Sided Bilayer Drawing
Nagamochi, Hiroshi
(2004)
Full text not available from this repository. ## AbstractGiven a bipartite graph G=(V,W,E), a bilayer drawing consists of placing nodes in the first vertex set V on a straight line L_1 and placing nodes in the second vertex set W on a parallel line L_2. The one-sided crossing minimization problem asks to find an ordering of nodes in V to be placed on L_1 so that the number of arc crossings is minimized. In this paper, we prove that there always exits a solution whose crossing number is at most 1.4664 times of a well-known lower bound that is obtained by summing up min{c_{uv}, c_{vu}} over all node pairs u, v \epsilon V, where c_uv denotes the number of crossings generated by arcs incident to u and v when u precedes v in an ordering.
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