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Approximate counting and sampling via local central limit theorems
[article]
2021
arXiv
pre-print
We give an FPTAS for computing the number of matchings of size k in a graph G of maximum degree Δ on n vertices, for all k ≤ (1-δ)m^*(G), where δ>0 is fixed and m^*(G) is the matching number of G, and an FPTAS for the number of independent sets of size k ≤ (1-δ) α_c(Δ) n, where α_c(Δ) is the NP-hardness threshold for this problem. We also provide quasi-linear time randomized algorithms to approximately sample from the uniform distribution on matchings of size k ≤ (1-δ)m^*(G) and independent
arXiv:2108.01161v1
fatcat:o4vpapffgvb3xj3hj433uzugha