Contracting planar graphs efficiently in parallel
We describe a new technique for contracting planar graphs which generalizes the tree contraction technique introduced by Miller and Reif. Our algorithm contracts a given planar graph in O(log n) rounds to one with a constant number of vertices. We use this technique to give an efficient NC solution to the following problem. It is known that a planar graph with n≥ 3 vertices has a straight-line embedding on an n−2 by n−2 grid. We show that such an embedding is computable in O(log2n log*n) time using O(n) processors on a CREW PRAM.
General TermsAlgorithms Theory
Additional Keywords and PhrasesPlanar graphs Fáry embeddings Parallel algorithms
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