Abstract
Abstract We propose several new heuristics for the twopage book crossing problem, which are based on recent algorithms for the corresponding one-page problem. Especially, the neural network model for edge allocation is combined for the first time with various one-page algorithms. We investigate the performance of the new heuristics by testing them on various benchmark test suites. It is found out that the new heuristics outperform the previously known heuristics and produce good approximations of the planar crossing number for severalwell-known graph families. We conjecture that the optimal two-page drawing of a graph represents the planar drawing of the graph.
Highlights
The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as halfcircles in κ half planes
The one-page [1] book crossing number corresponds to outerplanar [2] crossing number, which is the minimal number of edge crossings in a drawing where one places the vertices of a graph G along a circle, and the edges are drawn as straight lines
We have studied the two-page book crossing number problem using simulated annealing [19], genetic algorithm [20], and neural network [21]
Summary
The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as halfcircles in κ half planes (called pages). The one-page book crossing problem is equivalent to nding the order of the vertices on the circle which minimises the number of edge crossings. We further study heuristic algorithms that combine the latest one-page drawing algorithms (BB and AVSDF) [12, 13] and four edge allocation algorithms, such as SLOPE, LEN, CRS and the neural network (NN) model [21], for the two-page crossing number problem, and compare the performance of edge allocation algorithms. The goal of one-page algorithms is to order the vertices of a given graph to minimise the one-page book crossing number. CRS sorts the edges in non-increasing order of the number of crossings they produce, it nds the rst edge e in the list which would create fewer crossings on the other page, and moves it. The time complexity is O(m) excluding the computation of the number of crossings
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