### Abstract

We present a parallel organization with a reduced number of processors and special communication features for efficient solutions to problems in computational geometry. The organization has n processors operating in synchronous mode with row and column access to an n × n array of memory modules. The organization has simple regular structure and can be implemented in VLSI on a single chip or using a limited chip set. We develop fast parallel algorithms for computing several geometric properties of a set of n^{2} points in the plane. We present O(n log n) time parallel algorithms to compute the convex hull of n^{2} points in the plane, to compute the intersection of two convex polygons each having n^{2} edges, and to compute the diameter and a smallest enclosing box of a set of n^{2} points. All these problems require O(n^{2} log n) sequential time. Thus, all our solutions are optimal in the sense that their processor-time product is equal to the sequential complexity of these problems. We also consider the problem of computing nearest neighbors when the n^{2} points belong to an n × n digitized image. We show that this problem can be solved on the proposed parallel organization in O(n) time using n PEs, which is the same time taken by a two-dimensional mesh-connected computer with n^{2} processors to solve the same problem.

Original language | English |
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Pages (from-to) | 71-93 |

Number of pages | 23 |

Journal | Parallel Computing |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1989 |

Externally published | Yes |

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### Keywords

- computational geometry
- Parallel algorithms
- processor-time optimal solutions
- VLSI architecture

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Hardware and Architecture
- Computer Networks and Communications
- Computer Graphics and Computer-Aided Design
- Artificial Intelligence

### Cite this

*Parallel Computing*,

*12*(1), 71-93. https://doi.org/10.1016/0167-8191(89)90007-0