Optimal EREW parallel algorithms for connectivity, ear decomposition and st-numbering of planar graphs

Parallel EREW deterministic algorithms for finding the connected components, ear decomposition and st-numbering of a planar graph are presented. The algorithms take O(log(n)) time with _log(n)/^n+m processors. Previous results have the same complexity, but use the CRCW model. The same algorithms can be used for graphs with low genus. Let g be the genus of the minimal embedding of the graph, n the number of vertices and m the number of edges. The new algorithm takes T=O(log( n)+log²(g)) time and using optimal space and P=O(_log(n)/^n+m) processors