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An Improved Approximation to the One-Sided Bilayer Drawing

Nagamochi, Hiroshi (2004) An Improved Approximation to the One-Sided Bilayer Drawing. [Conference Paper]

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Abstract

Given 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.

Item Type:Conference Paper
Classifications:G Algorithms and Complexity > G.420 Crossings
M Methods > M.500 Layered
P Styles > P.480 Layered
ID Code:470
Deposited By:Selbach, Anna
Deposited On:09 Dec 2004
Last Modified:18 Sep 2008 13:08
Alternative Locations:http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=2912&spage=406

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