# 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 Citations (Scopus)

### 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 language English (US) 109-121 13 International Journal of Parallel Programming 21 2 https://doi.org/10.1007/BF01408289 Published - Apr 1 1992

### Fingerprint

Convex polygon
Parallel algorithms
Parallel Algorithms
Set of points
Polygon
Sequential Algorithm
Digital Image
Finite Set
Lower bound
Costs

### Keywords

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

### ASJC Scopus subject areas

• Theoretical Computer Science
• Software
• Information Systems

### Cite this

In: International Journal of Parallel Programming, Vol. 21, No. 2, 01.04.1992, p. 109-121.

Research output: Contribution to journalArticle

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