{"paper":{"title":"Superpolynomial smoothed complexity of 3-FLIP in Local Max-Cut","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Alex Scott, Lukas Michel","submitted_at":"2023-10-30T14:51:40Z","abstract_excerpt":"Local search algorithms for NP-hard problems such as Max-Cut frequently perform much better in practice than worst-case analysis suggests. Smoothed analysis has proved an effective approach to understanding this: a substantial literature shows that when a small amount of random noise is added to input data, local search algorithms typically run in polynomial or quasi-polynomial time. In this paper, we provide the first example where a local search algorithm for the Max-Cut problem fails to be efficient in the framework of smoothed analysis. Specifically, we construct a graph with $n$ vertices "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19594","kind":"arxiv","version":3},"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/2310.19594/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"}