An Analysis of Heuristics for Graph

We analyze several heuristics for graph planarization, i.e., deleting the minimum number of edges from a nonplanar graph to make it planar. The problem is NP-hard, although some heuristics which perform well in practice have been reported. In particular, we compare the two principle methods, based on path addition and vertex addition, respectively, with a selective edge addition method, an incremental method, and a \cycle packing" approach. For the incremental, the path addition, and the edge addition methods, we prove theoretical worst-case performance bounds of 1=3. We also present an empirical analysis of the heuristics. Our results indicate that the \cycle-packing" method consistently yields the best solutions when applied to a large set of test graphs.