Name
Abstract | ||
|---|---|---|
We develop a method for measuring homology classes. This involves two problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements' size have the minimal sum. We provide a greedy algorithm to compute the optimal basis and measure classes in it. The algorithm runs in O(@bn^3log^2n) time, where n is the size of the simplicial complex and @b is the Betti number of the homology group. Finally, we prove the stability of our result. The algorithm can be adapted to measure any given class. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.comgeo.2009.06.004 | Comput. Geom. |
Keywords | Field | DocType |
measure class,simplicial complex,finite field linear algebra,persistent homology,relative homology,homology class,minimal sum,computational geometry,homology group,greedy algorithm,computational topology computational geometry homology persistent homology homology basis stability finite field linear algebra,stability,natural generator,homology,homology basis,computational topology,optimal basis,betti number,linear algebra,finite field | Discrete mathematics,Combinatorics,Singular homology,Morse homology,Mayer–Vietoris sequence,Simplicial homology,Persistent homology,Cellular homology,Relative homology,CW complex,Mathematics | Journal |
Volume | Issue | ISSN |
43 | 2 | Computational Geometry: Theory and Applications |
Citations | PageRank | References |
15 | 0.78 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chao Chen | 1 | 2032 | 185.26 |
| Daniel Freedman | 2 | 517 | 27.79 |