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Contracting planar graphs efficiently in parallel

  • Martin Fürer
  • Balaji Raghavachari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 560)

Abstract

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 Terms

Algorithms Theory 

Additional Keywords and Phrases

Planar graphs Fáry embeddings Parallel algorithms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Martin Fürer
    • 1
  • Balaji Raghavachari
    • 1
  1. 1.Computer Science DepartmentPennsylvania State UniversityUniversity Park

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