Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays

Hussein Alnuweiri, Viktor K. Prasanna

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems on n×n images using a fixed-size linear array with p processors, where 1≤p≤n. O(n2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array with n processors can solve several image problems in O(n) time which is the same time taken by a two dimensional mesh-connected computer with n2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially in O(n)2) time, but require Ω(n2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization with p processors is proposed to solve such problems in O(n2/p) time, for 1≤p≤n.

Original languageEnglish
Pages (from-to)55-65
Number of pages11
JournalDistributed Computing
Volume5
Issue number2
DOIs
Publication statusPublished - 1 Sep 1991
Externally publishedYes

Fingerprint

Geometric Algorithms
Linear Array
Optimal Algorithm
Line
Communication
Parallel algorithms
Labeling
Partitioning
Mesh-connected Computer
Bandwidth
Computing
Convex Hull
Alternate
Rendering
Parallel Algorithms
Nearest Neighbor

Keywords

  • Image processing
  • Linear arrays
  • Optimal algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays. / Alnuweiri, Hussein; Prasanna, Viktor K.

In: Distributed Computing, Vol. 5, No. 2, 01.09.1991, p. 55-65.

Research output: Contribution to journalArticle

@article{87783d185fcb44aea69b5aaf3cfb9882,
title = "Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays",
abstract = "Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems on n×n images using a fixed-size linear array with p processors, where 1≤p≤n. O(n2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array with n processors can solve several image problems in O(n) time which is the same time taken by a two dimensional mesh-connected computer with n2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially in O(n)2) time, but require Ω(n2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization with p processors is proposed to solve such problems in O(n2/p) time, for 1≤p≤n.",
keywords = "Image processing, Linear arrays, Optimal algorithms",
author = "Hussein Alnuweiri and Prasanna, {Viktor K.}",
year = "1991",
month = "9",
day = "1",
doi = "10.1007/BF02259747",
language = "English",
volume = "5",
pages = "55--65",
journal = "Distributed Computing",
issn = "0178-2770",
publisher = "Springer Verlag",
number = "2",

}

TY - JOUR

T1 - Optimal geometric algorithms for digitized images on fixed-size linear arrays and scan-line arrays

AU - Alnuweiri, Hussein

AU - Prasanna, Viktor K.

PY - 1991/9/1

Y1 - 1991/9/1

N2 - Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems on n×n images using a fixed-size linear array with p processors, where 1≤p≤n. O(n2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array with n processors can solve several image problems in O(n) time which is the same time taken by a two dimensional mesh-connected computer with n2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially in O(n)2) time, but require Ω(n2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization with p processors is proposed to solve such problems in O(n2/p) time, for 1≤p≤n.

AB - Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems on n×n images using a fixed-size linear array with p processors, where 1≤p≤n. O(n2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array with n processors can solve several image problems in O(n) time which is the same time taken by a two dimensional mesh-connected computer with n2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially in O(n)2) time, but require Ω(n2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization with p processors is proposed to solve such problems in O(n2/p) time, for 1≤p≤n.

KW - Image processing

KW - Linear arrays

KW - Optimal algorithms

UR - http://www.scopus.com/inward/record.url?scp=34249923027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249923027&partnerID=8YFLogxK

U2 - 10.1007/BF02259747

DO - 10.1007/BF02259747

M3 - Article

AN - SCOPUS:34249923027

VL - 5

SP - 55

EP - 65

JO - Distributed Computing

JF - Distributed Computing

SN - 0178-2770

IS - 2

ER -