{"paper":{"title":"FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Tomohiro Koana","submitted_at":"2023-08-29T18:11:03Z","abstract_excerpt":"We study the \\textsc{$\\alpha$-Fixed Cardinality Graph Partitioning ($\\alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two numbers $k,p$ and $0\\leq\\alpha\\leq 1$, the question is whether there is a set $S\\subseteq V$ of size $k$ with a specified coverage function $cov_{\\alpha}(S)$ at least $p$ (or at most $p$ for the minimization version). The coverage function $cov_{\\alpha}(\\cdot)$ counts edges with exactly one endpoint in $S$ with weight $\\alpha$ and edges with both endpoints in $S$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15546","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/2308.15546/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"}