{"paper":{"title":"Approximate counting and sampling via local central limit theorems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.DS","authors_text":"Ashwin Sah, Mehtaab Sawhney, Vishesh Jain, Will Perkins","submitted_at":"2021-08-02T20:39:06Z","abstract_excerpt":"We give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\\Delta$ on $n$ vertices, for all $k \\le (1-\\delta)m^*(G)$, where $\\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an FPTAS for the number of independent sets of size $k \\le (1-\\delta) \\alpha_c(\\Delta) n$, where $\\alpha_c(\\Delta)$ 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 $k \\leq (1-\\delta)m^*(G)$ and independent sets of size $k \\leq (1-\\delta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01161","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.01161/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}