Approximating Simplet Frequency Distribution for Simplicial Complexes
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910344304132096 |
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| author | Beigy, Hamid Mahini, Mohammad Qadami, Salman Saghafian, Morteza |
| author_facet | Beigy, Hamid Mahini, Mohammad Qadami, Salman Saghafian, Morteza |
| contents | Simplets, constituting elementary units within simplicial complexes (SCs), serve as foundational elements for the structural analysis of SCs. Previous efforts have focused on the exact count or approximation of simplet count rather than their frequencies, with the latter being more practical in large-scale SCs. This paper enables simplet frequency analysis of SCs by introducing the Simplet Frequency Distribution (SFD) vector. In addition, we present a bound on the sample complexity required for accurately approximating the SFD vector by any uniform sampling-based algorithm. We also present a simple algorithm for this purpose and justify the theoretical bounds with experiments on some random simplicial complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximating Simplet Frequency Distribution for Simplicial Complexes Beigy, Hamid Mahini, Mohammad Qadami, Salman Saghafian, Morteza Computational Geometry Computational Complexity Geometric Topology 55-08 F.2 Simplets, constituting elementary units within simplicial complexes (SCs), serve as foundational elements for the structural analysis of SCs. Previous efforts have focused on the exact count or approximation of simplet count rather than their frequencies, with the latter being more practical in large-scale SCs. This paper enables simplet frequency analysis of SCs by introducing the Simplet Frequency Distribution (SFD) vector. In addition, we present a bound on the sample complexity required for accurately approximating the SFD vector by any uniform sampling-based algorithm. We also present a simple algorithm for this purpose and justify the theoretical bounds with experiments on some random simplicial complexes. |
| title | Approximating Simplet Frequency Distribution for Simplicial Complexes |
| topic | Computational Geometry Computational Complexity Geometric Topology 55-08 F.2 |
| url | https://arxiv.org/abs/2402.16777 |