2024/02/26 by Hamid Beigy, Mohammad Mahini, Beigy, Hamid +5
Computer Science · Mathematics · #55-08 #Advanced Algebra and Geometry #Computational Complexity (cs.CC) #Computational Geometry (cs.CG) #F.2 #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2402.16777
openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.