A neural-network algorithm for a graph layout problem

We present a neural-network algorithm for minimizing edge crossings in drawings of nonplanar graphs. This is an important subproblem encountered in graph layout. The algorithm finds either the minimum number of crossings or an approximation thereof and also provides a linear embedding realizing the number of crossings found. The parallel time complexity of the algorithm is O(1) for a neural network with n/sup 2/ processing elements, where n is the number of vertices of the graph. We present results from testing a sequential simulator of the algorithm on a set of nonplanar graphs and compare its performance with the heuristic of Nicholson.