An optimal parallel algorithm for planar cycle separators

We present an optimal parallel algorithm for computing a cycle separator of ann-vertex embedded planar undirected graph inO(logn) time onn/logn processors. As a consequence, we also obtain an improved parallel algorithm for constructing a depth-first search tree rooted at any given vertex in a connected planar undirected graph in O(log2n) time on n/logn processors. The best previous algorithms for computing depth-first search trees and cycle separators achieved the same time complexities, but withn processors. Our algorithms run on a parallel random access machine that permits concurrent reads and concurrent writes in its shared memory and allows an arbitrary processor to succeed in case of a write conflict.

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