Name
Abstract | ||
|---|---|---|
We develop a method for measuring homology classes. This involves three 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(beta(4)n(3) log(2) n) time, where n is the size of the simplicial complex and beta is the Betti number of the homology group. Third, we discuss different ways of localizing homology classes and prove some hardness results. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.4230/LIPIcs.STACS.2008.1343 | STACS 2008: PROCEEDINGS OF THE 25TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE |
Keywords | DocType | Volume |
computational topology,computational geometry,homology,persistent homology,localization,optimization | Journal | abs/0802.2865 |
ISSN | Citations | PageRank |
Dans Proceedings of the 25th Annual Symposium on the Theoretical
Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) | 12 | 0.90 |
References | Authors | |
13 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chao Chen | 1 | 2032 | 185.26 |
| Daniel Freedman | 2 | 517 | 27.79 |