Quantifying Homology Classes
| dc.creator | Chen, Chao | |
| dc.creator | Freedman, Daniel | |
| dc.date | 2008-02-20 | |
| dc.date.accessioned | 2026-07-07T09:22:04Z | |
| dc.date.available | 2026-07-07T09:22:04Z | |
| dc.description | 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 $O(β^4 n^3 \log^2 n)$ time, where $n$ is the size of the simplicial complex and $β$ is the Betti number of the homology group. Third, we discuss different ways of localizing homology classes and prove some hardness results. | |
| dc.identifier | https://arxiv.org/abs/0802.2865 | |
| dc.identifier | http://arxiv.org/abs/0802.2865 | |
| dc.identifier | Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155249 | |
| dc.subject | Computational Geometry | |
| dc.subject | Discrete Mathematics | |
| dc.title | Quantifying Homology Classes | |
| dc.type | text |