Branch-and-Bound Techniques for the Maximum Planar Subgraph Problem

We present branch-and-bound algorithms for nding a maximum planar subgraph of a nonplanar graph. The problem has important applications in circuit layout, automated graph drawing, and facility layout. The algorithms described utilize heuristics to obtain an initial lower bound for the size of a maximum planar subgraph, then apply a sequence of fast preliminary tests for planarity to eliminate infeasible partial solutions. Computational experience is reported from testing the algorithms on a set of random nonplanar graphs and is encouraging. A best-rst search technique is shown to be a practical approach to solving problems of moderate size.