Parallel Algorithms for Arrangements

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 of O(log n log n) time and n2/ log n processors. We generalize this to obtain an O(log n log n)-time algorithm using nd / log n processors for solving the problem in d dimensions. We also give a randomized algorithm for the EREW PRAM that constructs an arrangement of n lines on-line, in which each insertion is done in optimal O(log n) time using n/ log n 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.

• Type: Conference
• Year: 1990
• Where: SPAA
• Authors: Richard J. Anderson, Paul Beame, Erik Brisson
• Keywords: Algorithms, Arrangement Problem, Distributed And Parallel Computing, Parallel Algorithms, SPAA 1990