Treffer: 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms

We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing their results to optimum solutions. Key words: Automatic Graph Drawing, Crossing Minimization, Linear Ordering, Polyhedral Combinatorics, Branch and Cut 1. Introduction Directed graphs are widely used to represent structures in many fields such as economics, social sciences, mathematics and computer science. A good visualization of structural information allows the reader to focus on the inform.