Crossing Reduction by Windows Optimization

Abstract

The number of edge crossings is a commonly accepted measure to judge the "readability" of graph drawings. In this paper we present a new algorithm for high quality multi-layer straight-line crossing minimization. The proposed method uses a local optimization technique where subsets of nodes and edges are processed exactly. The algorithm uses optimization on a window applied in a manner, similar to those used in the area of formal verification of logic circuits. In contrast to most existing heuristics, more than two layers are considered simultaneously. The algorithm tries to reduce the total number of crossings based on an initial placement of the nodes and can thus also be used in a postprocessing step. Experiments are given to demonstrate the efficacy of the proposed technique on benchmarks from the area of circuit design.

An Experimental Study of Crossing Minimization Heuristics

“…Both algorithms are rather of theoretical nature and have so far not been useful for solving practical instances. Much easier to tackle is the bipartite crossing number, for which a vast amount of experimental papers exist in the literature (see, e.g., [16,7]). Experimental papers in other fields include, e.g., a collection of experimental studies in graph drawing by Vismara et al [24] and the paper by Brandenburg et al on force-directed methods [4].…”

Minimizing crossings in hierarchical digraphs with a hybridized genetic algorithm

“…The averaging heuristics reported in the introduction are known for computing solutions in a short time. Although more complex approaches coming originally from circuit design have been recently proposed (Eschbach et al, 2002;Matuszewski et al, 1999), we here restrict ourselves to the original ones which are the most popular. Hence, the considered local search strategy combines the greedy-switch heuristics and adaptive versions of the median and the barycenter heuristics for each layer.…”

Confluent Layered Drawings

“…They conclude that if the permutation of one layer is fixed, there is no need for heuristics, and in the case where both layers are not fixed, the iterated barycenter method is the best among several heuristics. Recently new methods related to crossing reduction [1], [8], [10], [24], [27] have been proposed.…”