Paper Info
Title
Computing homology: a global reduction approach
Abstract
A new algorithm to compute the homology of a finitely generated chain complex is proposed in this work. It is based on grouping algebraic reductions of the complex into structures that can be encoded as directed acyclic graphs. This leads to sequences of projection maps that reduce the number of generators in the complex while preserving its homology. This organization of reduction pairs allows to update the boundary information in a single step for a whole set of reductions which shows impressive gains in computational performance compared to existing methods. In addition, this method gives the homology generators for a small additional cost.
Year
DOI
Venue
2009
10.1007/978-3-642-04397-0_27
DGCI
Keywords
Field
DocType
reduction pair,algebraic reduction,acyclic graph,computing homology,impressive gain,boundary information,computational performance,global reduction approach,new algorithm,chain complex,projection map,homology generator,directed acyclic graph,group algebra
Discrete mathematics,Graph,Topology,Combinatorics,Finitely-generated abelian group,Algebraic number,Computer science,Directed acyclic graph,Relative homology,Cellular homology,Homology (biology),CW complex
Conference
Volume
ISSN
ISBN
5810
0302-9743
3-642-04396-8
Citations 
PageRank 
References 
0
0.34
9
Authors
2
Name
Order
Citations
PageRank
David Corriveau1213.64
Madjid Allili2468.64