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arXiv · 1702.06632

Novel Algorithms for Sampling Abstract Simplicial Complexes

John Lombard
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Abstract

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.

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John Lombard. 2017-02-22. Novel Algorithms for Sampling Abstract Simplicial Complexes. https://arxiv.org/abs/1702.06632

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