A simple sub-quadratic algorithm for computing the subset partial order

A given collection of sets has a natural partial order induced by the subset relation. Let the size N of the collection be defined as the sum of the cardinalities of the sets that comprise it. Algorithms have recently been presented that compute the partial order (and thereby the minimal and maximal...

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Bibliographic Details
Published in:Information processing letters Vol. 56; no. 6; pp. 337 - 341
Main Author: Pritchard, Paul
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 22.12.1995
Elsevier Science
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Extremal sets
Lexicographic order
Mathematical logic, foundations, set theory
Mathematics
Sciences and techniques of general use
Set theory
Set-theoretic algorithms
Subset graph
Subset partial order
Theoretical computing
Set-theoretic algorithms
Extremal sets
Subset partial order
Algorithms
Lexicographic order
Subset graph
Subset relation
Partial ordering
Set theory
Algorithm complexity
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:A given collection of sets has a natural partial order induced by the subset relation. Let the size N of the collection be defined as the sum of the cardinalities of the sets that comprise it. Algorithms have recently been presented that compute the partial order (and thereby the minimal and maximal sets, i.e., extremal sets) in worst-case time O( N 2 log N ) . This paper develops a simple algorithm that uses only simple data structures, and gives a simple analysis that establishes the above worst-case bound on its running time. The algorithm exploits a variation on lexicographic order that may be of independent interest.
ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(95)00165-4