An old sub-quadratic algorithm for finding extremal sets

Some previously proposed algorithms are re-examined. They were designed to find all sets in a collection that have no subset in the collection, but are easily modified to find all sets that have no supersets. One is shown to have a worst-case running-time of O (N-squared / log N), where N is the sum...

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Bibliographic Details
Published in:Information processing letters Vol. 62; no. 6; pp. 329 - 334
Main Author: PRITCHARD, P
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Science 27.06.1997
Elsevier Sequoia S.A
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Information processing
Mathematical analysis
Studies
Theoretical computing
Set theory
Extremal set
Algorithms
Combinatorial problem
Algorithm analysis
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:Some previously proposed algorithms are re-examined. They were designed to find all sets in a collection that have no subset in the collection, but are easily modified to find all sets that have no supersets. One is shown to have a worst-case running-time of O (N-squared / log N), where N is the sum of the sizes of all the sets. This is lower than the only previously known sub-quadratic worst-case upper bound for this problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0020-0190
1872-6119
DOI:10.1016/s0020-0190(97)00084-7