A Log-space Algorithm for Canonization of Planar Graphs

Planar graph canonization is known to be hard for L this directly follows from L-hardness of tree-canonization [Lin92]. We give a log-space algorithm for planar graph canonization. This gives completeness for log-space under AC many-one reductions and improves the previously known upper bound of AC [MR91]. A planar graph can be decomposed into biconnected components. We give a log-space procedure for the decomposition of a biconnected planar graph into a triconnected component tree. The canonization process is based on these decomposition steps.