Parallel algorithms for separation of two sets of points and recognition of digital convex polygons

Dilip Sarkar, Ivan Stojmenović

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Given two finite sets of points in a plane, the polygon separation problem is to construct a separating convex k-gon with smallest k. In this paper, we present a parallel algorithm for the polygon separation problem. The algorithm runs in O(log n) time on a CREW PRAM with n processors, where n is the number of points in the two given sets. The algorithm is cost-optimal, since Ω(n log n) is a lower-bound for the time needed by any sequential algorithm. We apply this algorithm to the problem of finding a convex polygon, with the minimal number of edges, for which a given convex region is its digital image. The algorithm in this paper constructs one such polygon with possibly two more edges than the minimal one.

Original languageEnglish (US)
Pages (from-to)109-121
Number of pages13
JournalInternational Journal of Parallel Programming
Volume21
Issue number2
DOIs
StatePublished - Apr 1 1992

Keywords

  • Algorithms
  • PRAMs
  • computational geometry
  • digital polygons
  • parallel algorithms

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Information Systems

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