Coreduction Homology Algorithm

This paper presents a new reduction algorithm for the efficient computation of the homology of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets embedded in high dimensions—runs in linear time. The paper presents the theoretical background of the algorithm, the a...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 41; no. 1; pp. 96 - 118
Main Authors Mrozek, Marian, Batko, Bogdan
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 2009
Springer Nature B.V
Subjects
Algorithms
Combinatorics
Computational Mathematics and Numerical Analysis
Geometry
Mathematics
Mathematics and Statistics
Reduction methods
Homology algorithm
Cubical set
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Summary:This paper presents a new reduction algorithm for the efficient computation of the homology of cubical sets and polotypes. The algorithm—particularly strong for low-dimensional sets embedded in high dimensions—runs in linear time. The paper presents the theoretical background of the algorithm, the algorithm itself, experimental results based on an implementation for cubical sets as well as some theoretical complexity estimates.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-008-9073-y