### 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) |
---|---|

Pages (from-to) | 109-121 |

Number of pages | 13 |

Journal | International Journal of Parallel Programming |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 1992 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Information Systems

### Cite this

*International Journal of Parallel Programming*,

*21*(2), 109-121. https://doi.org/10.1007/BF01408289

**Parallel algorithms for separation of two sets of points and recognition of digital convex polygons.** / Sarkar, Dilip; Stojmenović, Ivan.

Research output: Contribution to journal › Article

*International Journal of Parallel Programming*, vol. 21, no. 2, pp. 109-121. https://doi.org/10.1007/BF01408289

}

TY - JOUR

T1 - Parallel algorithms for separation of two sets of points and recognition of digital convex polygons

AU - Sarkar, Dilip

AU - Stojmenović, Ivan

PY - 1992/4/1

Y1 - 1992/4/1

N2 - 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.

AB - 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.

KW - Algorithms

KW - computational geometry

KW - digital polygons

KW - parallel algorithms

KW - PRAMs

UR - http://www.scopus.com/inward/record.url?scp=24944548143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944548143&partnerID=8YFLogxK

U2 - 10.1007/BF01408289

DO - 10.1007/BF01408289

M3 - Article

AN - SCOPUS:24944548143

VL - 21

SP - 109

EP - 121

JO - International Journal of Parallel Programming

JF - International Journal of Parallel Programming

SN - 0885-7458

IS - 2

ER -