Improved Parallel Depth-First Search in Undirected Planar Graphs

We present an improved parallel algorithm for constructing a depth-first search tree in a connected undirected planar graph. The algorithm runs in O(log2n) time with n/log n processors for an n-vertex graph. It hinges on the use of a new optimal algorithm for computing a cycle separator of an embedded planar graph in O(log n) time with n/log n processors. The best previous algorithms for computing depth-first search trees and cycle separators achieved the same time complexities, but with n 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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