PLANAR STRONG CONNECTIVITY HELPS IN PARALLEL DEPTH-FIRST SEARCH

This paper proves that for a strongly connected planar directed graph of size n, a depth-first search tree rooted at a specified vertex can be computed in O(log(5) n) time with n/log n processors. Previously, for planar directed graphs that may not be strongly connected, the best depth-first search algorithm runs in O(log(10) n) time with n processors. Both algorithms run on a parallel random access machine that allows concurrent reads and concurrent writes in its shared memory, and in case of a write conflict, permits an arbitrary processor to succeed.