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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Vydané v:	International journal of computer mathematics Ročník 37; číslo 1-2; s. 49 - 61
Hlavní autori:	Datta, Amitava, Srikant, R., Krithivasan, Kamala
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Abingdon Gordon and Breach Science Publishers 01.01.1990 Taylor and Francis
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Srikant, R. Krithivasan, Kamala Datta, Amitava
Author_xml	– sequence: 1 givenname: Amitava surname: Datta fullname: Datta, Amitava organization: Department of Computer Science and Engineering , Indian Institute of Technology – sequence: 2 givenname: R. surname: Srikant fullname: Srikant, R. organization: Department of Computer Science and Engineering , Indian Institute of Technology – sequence: 3 givenname: Kamala surname: Krithivasan fullname: Krithivasan, Kamala organization: Department of Computer Science and Engineering , Indian Institute of Technology
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References	Datta A.. (CIT0008) CIT0012 CIT0011 Kruskal C.P. (CIT0010) 1985; 34 Ullman J.D. (CIT0013) 1984 CIT0003 CIT0002 CIT0005 CIT0004 CIT0007 CIT0006 CIT0009 Aggarwal A. (CIT0001) 1989; 39
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Title	Fast sequential and parallel algorithms for finding the largest rectangle separating two sets
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