Coreduction Homology Algorithm

Authors:
Marian Mrozek;Bogdan Batko
Affiliations:
Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30-072, Kraków, Poland and Graduate School of Business, Division of Computational Mathematics, ul. Zielona 27, 33-300 ...;Graduate School of Business, Division of Computational Mathematics, ul. Zielona 27, 33-300, Nowy Sa̧cz, Poland and Pedagogical University, Institute of Mathematics, ul. Podchora̧� ...
Venue:
Discrete & Computational Geometry
Year:
2009

Citing 0
Cited 7

Detecting pathologies with homology algorithms in magnetic resonance images of brain

Machine Graphics & Vision International Journal
Computing homology: a global reduction approach

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Coreduction homology algorithm for inclusions and persistent homology

Computers & Mathematics with Applications
Critical Analysis of the Spanning Tree Techniques

SIAM Journal on Numerical Analysis
A global method for reducing multidimensional size graphs

GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
A fast algorithm to compute cohomology group generators of orientable 2-manifolds

Pattern Recognition Letters
Homology computations via acyclic subspace

CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.