Fast sequential and parallel algorithms for finding the largest rectangle separating two sets

Given a bounding isothetic rectangle BR and two sets of points A and B with cardinalities n and m inside it, we have to find an isothetic rectangle containing maximum number of points from set A and no point from set B. We consider two limiting cases of this problem when the cardinalities of set A (...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 37; no. 1-2; pp. 49 - 61
Main Authors: Datta, Amitava, Srikant, R., Krithivasan, Kamala
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers 01.01.1990
Taylor and Francis
Subjects:
1.3.5 [Computational Geometry and Object Modelling]
Applied sciences
Artificial intelligence
B.7.1 [Very Large Scale Integration]
C.1.1 [Single Data Stream Architcctures]
Computational geometry
Computer science; control theory; systems
CREW PRAM
Exact sciences and technology
F.2.2 [Analysis of Algorithms and Problem Complexity]
isothetic rectangles
line sweep paradigm
Pattern recognition. Digital image processing. Computational geometry
systolic array
Computational geometry
Parallel algorithm
Fast algorithm
Algorithm analysis
Algorithm complexity
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:Given a bounding isothetic rectangle BR and two sets of points A and B with cardinalities n and m inside it, we have to find an isothetic rectangle containing maximum number of points from set A and no point from set B. We consider two limiting cases of this problem when the cardinalities of set A (resp. set B) is much greater than that of set B (resp. set ,A). We present efficient sequential and parallel algorithms for these two problems. Our sequential algorithms run in O((n + m)log m + m 2 ) and O((m+ n) log n + n 2 ) time respectively. The parallel algorithms in CREW PRAM run in o(log n) ando(log m 2 ) time using O(max(n,m 2 /logm)) and O(max(m,n 2 /logn)) processors respectively. Our sequential algorithms are faster than a previous algorithm under these constraints on cardinality. No previous parallel algorithm was known for this problem. We also present an optimal systolic algorithm for the original problem.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169008803934