Parallel geometric algorithms on a mesh-connected computer

Chang-Sung Jeong, D. T. Lee

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

Original languageEnglish
Pages (from-to)155-177
Number of pages23
JournalAlgorithmica
Volume5
Issue number1-4
DOIs
Publication statusPublished - 1990 Jun 1
Externally publishedYes

Fingerprint

Mesh-connected Computer
Geometric Algorithms
Parallel algorithms
Parallel Algorithms
Circle
Intersection
Point Location
Convex polygon
Divide and conquer
Voronoi Diagram
Decomposition
Decompose

Keywords

  • Computational geometry
  • Mesh-connected computer
  • Multipoint location
  • Parallel algorithms
  • Voronoi diagrams

ASJC Scopus subject areas

  • Applied Mathematics
  • Safety, Risk, Reliability and Quality
  • Software
  • Computer Graphics and Computer-Aided Design

Cite this

Parallel geometric algorithms on a mesh-connected computer. / Jeong, Chang-Sung; Lee, D. T.

In: Algorithmica, Vol. 5, No. 1-4, 01.06.1990, p. 155-177.

Research output: Contribution to journalArticle

Jeong, Chang-Sung ; Lee, D. T. / Parallel geometric algorithms on a mesh-connected computer. In: Algorithmica. 1990 ; Vol. 5, No. 1-4. pp. 155-177.
@article{fff8567376324d288de9daab9dd12ebe,
title = "Parallel geometric algorithms on a mesh-connected computer",
abstract = "We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.",
keywords = "Computational geometry, Mesh-connected computer, Multipoint location, Parallel algorithms, Voronoi diagrams",
author = "Chang-Sung Jeong and Lee, {D. T.}",
year = "1990",
month = "6",
day = "1",
doi = "10.1007/BF01840383",
language = "English",
volume = "5",
pages = "155--177",
journal = "Algorithmica",
issn = "0178-4617",
publisher = "Springer New York",
number = "1-4",

}

TY - JOUR

T1 - Parallel geometric algorithms on a mesh-connected computer

AU - Jeong, Chang-Sung

AU - Lee, D. T.

PY - 1990/6/1

Y1 - 1990/6/1

N2 - We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

AB - We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) in O(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. The O(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.

KW - Computational geometry

KW - Mesh-connected computer

KW - Multipoint location

KW - Parallel algorithms

KW - Voronoi diagrams

UR - http://www.scopus.com/inward/record.url?scp=52449146405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449146405&partnerID=8YFLogxK

U2 - 10.1007/BF01840383

DO - 10.1007/BF01840383

M3 - Article

VL - 5

SP - 155

EP - 177

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1-4

ER -