@inproceedings{4ce2e9fe03cb4337970ead67ddcf2665,
title = "Quantifying homology classes",
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(β4n3 log2 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.",
keywords = "Computational geometry, Computational topology, Homology, Localization, Optimization, Persistent homology",
author = "Chao Chen and Daniel Freedman",
year = "2008",
language = "English",
isbn = "9783939897064",
series = "Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008",
publisher = "IBFI Schloss Dagstuhl",
pages = "169--180",
booktitle = "Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008",
note = "25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008 ; Conference date: 21-02-2008 Through 23-02-2008",
}