### 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 |
---|---|

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 |

### Fingerprint

### 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

**An efficient VLSI architecture with applications to geometric problems.** / Alnuweiri, Hussein; Prasanna Kumar, V. K.

Research output: Contribution to journal › Article

*Parallel Computing*, vol. 12, no. 1, pp. 71-93. https://doi.org/10.1016/0167-8191(89)90007-0

}

TY - JOUR

T1 - An efficient VLSI architecture with applications to geometric problems

AU - Alnuweiri, Hussein

AU - Prasanna Kumar, V. K.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - 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 n2 points in the plane. We present O(n log n) time parallel algorithms to compute the convex hull of n2 points in the plane, to compute the intersection of two convex polygons each having n2 edges, and to compute the diameter and a smallest enclosing box of a set of n2 points. All these problems require O(n2 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 n2 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 n2 processors to solve the same problem.

AB - 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 n2 points in the plane. We present O(n log n) time parallel algorithms to compute the convex hull of n2 points in the plane, to compute the intersection of two convex polygons each having n2 edges, and to compute the diameter and a smallest enclosing box of a set of n2 points. All these problems require O(n2 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 n2 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 n2 processors to solve the same problem.

KW - computational geometry

KW - Parallel algorithms

KW - processor-time optimal solutions

KW - VLSI architecture

UR - http://www.scopus.com/inward/record.url?scp=0024751915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024751915&partnerID=8YFLogxK

U2 - 10.1016/0167-8191(89)90007-0

DO - 10.1016/0167-8191(89)90007-0

M3 - Article

VL - 12

SP - 71

EP - 93

JO - Parallel Computing

JF - Parallel Computing

SN - 0167-8191

IS - 1

ER -