{"paper":{"title":"A Tolerant Independent Set Tester","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cameron Seth","submitted_at":"2025-03-27T12:34:48Z","abstract_excerpt":"We give nearly optimal bounds on the sample complexity of $(\\widetilde{\\Omega}(\\epsilon),\\epsilon)$-tolerant testing the $\\rho$-independent set property in the dense graph setting. In particular, we give an algorithm that inspects a random subgraph on $\\widetilde{O}(\\rho^3/\\epsilon^2)$ vertices and, for some constant $c,$ distinguishes between graphs that have an induced subgraph of size $\\rho n$ with fewer than $\\frac{\\epsilon}{c \\log^4(1/\\epsilon)} n^2$ edges from graphs for which every induced subgraph of size $\\rho n$ has at least $\\epsilon n^2$ edges. Our sample complexity bound matches, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21441","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/2503.21441/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"}