An Efficient Algorithm for 1-Dimensional (Persistent) Path Homology

نویسندگان

چکیده

This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from topological viewpoint. A prevalent technique such analysis involves computation of homology groups and their persistence. These concepts are well suited spaces that not directed. As result, one needs concept accommodates orientations in input space. Path-homology developed graphs by Grigoryan et al. (2012) has been effectively adapted this purpose recently Chowdhury Mémoli (2018). They also give to compute the path-homology persistent path-homology. Our main contribution is computes its persistence more efficiently 1-dimensional (\(H_1\)) case. In algorithm, we discover various structures computations aid computing We implement our present some preliminary experimental results.

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ژورنال

عنوان ژورنال: Discrete and Computational Geometry

سال: 2022

ISSN: ['1432-0444', '0179-5376']

DOI: https://doi.org/10.1007/s00454-022-00430-8