Various heuristic algorithms to minimise the two-page crossingnumbers of graphs

We propose several new heuristics for the two-page 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 several wellknown graph families. We conjecture that the optimal two-page drawing of a graph represents the planar drawing of the graph.