Buchheim, Christoph and Zheng, Lanbo (2006) Fixed Linear Crossing Minimization by Reduction to the Maximum Cut Problem.
Published In: Computing and combinatorics : 12th annual international conference, COCOON 2006, Taipei, Taiwan, August 15 - 18, 2006 ; proceedings, Lecture Notes in Computer Science. 4112 Springer 2006, pp. 507-516.

Abstract

Many real-life scheduling, routing and locating 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 NP-hard problem can be reduced to the well-known maximum cut problem. The latter problem was intensively studied in the literature; practically efficient exact algorithms based on the branch-and-cut technique have been developed. By an experimental evaluation on a variety of graphs, we prove that using this reduction for solving FLCNP compares favorably to earlier branch-and-bound algorithms.

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