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Algorithmica

, Volume 15, Issue 2, pp 104–125 | Cite as

Parallel algorithms for arrangements

  • R. Anderson
  • P. Beanie
  • E. Brisson
Article

Abstract

We give the first efficient parallel algorithms for solving the arrangement problem. We give a deterministic algorithm for the CREW PRAM which runs in nearly optimal bounds ofO (logn log*n) time andn2/logn processors. We generalize this to obtain anO (logn log*n)-time algorithm usingn d /logn processors for solving the problem ind dimensions. We also give a randomized algorithm for the EREW PRAM that constructs an arrangement ofn lines on-line, in which each insertion is done in optimalO (logn) time usingn/logn processors. Our algorithms develop new parallel data structures and new methods for traversing an arrangement.

Key words

Parallel algorithms Computational geometry Arrangement problem Incremental algorithms 

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Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • R. Anderson
    • 1
  • P. Beanie
    • 1
  • E. Brisson
    • 1
  1. 1.Department of Computer Science and Engineering, FR-35University of WashingtonSeattleUSA

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