{"paper":{"title":"The Limits of Local Search for the Maximum Weight Independent Set Problem in d-Claw Free Graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Meike Neuwohner","submitted_at":"2021-06-07T12:35:29Z","abstract_excerpt":"We consider the Maximum Weight Independent Set Problem (MWIS) in $d$-claw free graphs, i.e. the task of computing an independent set of maximum weight in a given $d$-claw free graph $G=(V,E)$ equipped with a positive weight function $w:V\\rightarrow\\mathbb{R}_{>0}$. For $k\\geq 1$, the MWIS in $k+1$-claw free graphs generalizes the weighted $k$-Set Packing Problem. Given that for $k\\geq 3$, this problem does not permit a polynomial time $o(\\frac{k}{\\log k})$-approximation unless $P=NP$, most previous algorithms for both weighted $k$-Set Packing and the MWIS in $d$-claw free graphs rely on local "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03555","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/2106.03555/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"}