Given a simplicial complex and a vector-valued function on its vertices, we present an algorithmic construction of an acyclic partial matching on the cells of the complex. This construction is used to build a reduced filtered complex with the same multidimensional persistent homology as of the original one filtered by the sublevel sets of the function. A number of numerical experiments show a substantial rate of reduction in the number of cells achieved by the algorithm.
Algorithmic Construction of Acyclic Partial Matchings for Multidimensional Persistence / Allili, Madjid; Kaczynski, Tomasz; Landi, Claudia; Masoni, Filippo. - 10502:(2017), pp. 375-387. (Intervento presentato al convegno 20th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2017 tenutosi a Vienna (A) nel 19-21 settembre 2017) [10.1007/978-3-319-66272-5_30].
Algorithmic Construction of Acyclic Partial Matchings for Multidimensional Persistence
LANDI, Claudia;
2017
Abstract
Given a simplicial complex and a vector-valued function on its vertices, we present an algorithmic construction of an acyclic partial matching on the cells of the complex. This construction is used to build a reduced filtered complex with the same multidimensional persistent homology as of the original one filtered by the sublevel sets of the function. A number of numerical experiments show a substantial rate of reduction in the number of cells achieved by the algorithm.
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