### Abstract

Efficient implementation of global computations on a, linear array of processors is complicated due to the small communication bandwidth and the large communication diameter of the array. This paper presents efficient parallel techniques for partitioning, movement, and reduction of data on linear arrays. Also, efficient data structures are used to enable fast sequential access of query points within each processor. This combination of serial and parallel techniques is used to derive an optimal parallel algorithm for computing the convex hull of each connected region in an n × n image. The algorithm takes O(n^{2}/p) time on a linear array with p processors, where 1 ≤ p ≤ n/logn. This result is processor-time optimal since an optimal sequential algorithm takes O(n^{2}) to solve the problem. Thus, a linear array with n/log n processors can solve the above problem in O(nlogn) time. In comparison, a two dimensional mesh-connected array of processors can solve this problem in O(n) time using n2 processors. The processor-time product for the mesh is 0(n^{3}), which is not optimal.

Original language | English |
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Title of host publication | Algorithms - International Symposium SlGAL 1990, Proceedings |

Publisher | Springer Verlag |

Pages | 397-406 |

Number of pages | 10 |

ISBN (Print) | 9783540529217 |

DOIs | |

Publication status | Published - 1 Jan 1990 |

Externally published | Yes |

Event | 1st SIGAL International Symposium on Algorithms, 1990 - Tokyo, Japan Duration: 16 Aug 1990 → 18 Aug 1990 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 450 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st SIGAL International Symposium on Algorithms, 1990 |
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Country | Japan |

City | Tokyo |

Period | 16/8/90 → 18/8/90 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms - International Symposium SlGAL 1990, Proceedings*(pp. 397-406). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 450 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-52921-7_89

**Parallel convexity algorithms for digitized images on a linear array of processors.** / Alnuweiri, Hussein; Prasanna Kumar, V. K.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms - International Symposium SlGAL 1990, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 450 LNCS, Springer Verlag, pp. 397-406, 1st SIGAL International Symposium on Algorithms, 1990, Tokyo, Japan, 16/8/90. https://doi.org/10.1007/3-540-52921-7_89

}

TY - GEN

T1 - Parallel convexity algorithms for digitized images on a linear array of processors

AU - Alnuweiri, Hussein

AU - Prasanna Kumar, V. K.

PY - 1990/1/1

Y1 - 1990/1/1

N2 - Efficient implementation of global computations on a, linear array of processors is complicated due to the small communication bandwidth and the large communication diameter of the array. This paper presents efficient parallel techniques for partitioning, movement, and reduction of data on linear arrays. Also, efficient data structures are used to enable fast sequential access of query points within each processor. This combination of serial and parallel techniques is used to derive an optimal parallel algorithm for computing the convex hull of each connected region in an n × n image. The algorithm takes O(n2/p) time on a linear array with p processors, where 1 ≤ p ≤ n/logn. This result is processor-time optimal since an optimal sequential algorithm takes O(n2) to solve the problem. Thus, a linear array with n/log n processors can solve the above problem in O(nlogn) time. In comparison, a two dimensional mesh-connected array of processors can solve this problem in O(n) time using n2 processors. The processor-time product for the mesh is 0(n3), which is not optimal.

AB - Efficient implementation of global computations on a, linear array of processors is complicated due to the small communication bandwidth and the large communication diameter of the array. This paper presents efficient parallel techniques for partitioning, movement, and reduction of data on linear arrays. Also, efficient data structures are used to enable fast sequential access of query points within each processor. This combination of serial and parallel techniques is used to derive an optimal parallel algorithm for computing the convex hull of each connected region in an n × n image. The algorithm takes O(n2/p) time on a linear array with p processors, where 1 ≤ p ≤ n/logn. This result is processor-time optimal since an optimal sequential algorithm takes O(n2) to solve the problem. Thus, a linear array with n/log n processors can solve the above problem in O(nlogn) time. In comparison, a two dimensional mesh-connected array of processors can solve this problem in O(n) time using n2 processors. The processor-time product for the mesh is 0(n3), which is not optimal.

UR - http://www.scopus.com/inward/record.url?scp=85031809173&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031809173&partnerID=8YFLogxK

U2 - 10.1007/3-540-52921-7_89

DO - 10.1007/3-540-52921-7_89

M3 - Conference contribution

AN - SCOPUS:85031809173

SN - 9783540529217

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 397

EP - 406

BT - Algorithms - International Symposium SlGAL 1990, Proceedings

PB - Springer Verlag

ER -