Fixed linear crossing minimization by reduction to the maximum cut problem
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| Venue: | in Proc 12th Ann. Int. Computing and Combinatorics Conference (COCOON’06 |
| Citations: | 2 - 0 self |
BibTeX
@INPROCEEDINGS{Buchheim_fixedlinear,
author = {Christoph Buchheim and Lanbo Zheng},
title = {Fixed linear crossing minimization by reduction to the maximum cut problem},
booktitle = {in Proc 12th Ann. Int. Computing and Combinatorics Conference (COCOON’06},
year = {}
}
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Abstract
Abstract. Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a way that the number of edge crossings is minimized. In this paper, we study a restricted version of the linear layout problem where the order of vertices on the line is fixed, the so-called fixed linear crossing number problem (FLCNP). We show that this N P-hard problem can be reduced to the well-known maximum cut problem. The latter problem was intensively studied in the literature; efficient exact algorithms based on the branch-and-cut technique have been developed. By an experimental evaluation on a variety of graphs, we show that using this reduction for solving FLCNP compares favorably to earlier branch-and-bound algorithms. 1
