2017/02/22 by John Lombard, Lombard, John
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1702.06632
openalex publication_date 2017/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide dual algorithms for sampling the space of abstract simplicial complexes on a fixed number of vertices. We develop a generative and descriptive sampler designed with heuristics to help balance the combinatorial multiplicities of the states and more widely sample across the space of nonisomorphic complexes. We provide a formula for the exact probabilities with which this algorithm will produce a requested labeled state, and compare with an existing benchmark. We also design a highly conductive local ergodic random walk with known transition probabilities. We characterize the autocorrelation of the walk, and numerically test it against our sampler to illustrate its efficacy.