{"paper":{"title":"Approximation algorithm for the Multicovering Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Abbass Gorgi, Anand Srivastav, Mohamed Hachimi, Mourad El Ouali","submitted_at":"2020-03-15T22:07:13Z","abstract_excerpt":"Let $\\mathcal{H}=(V,\\mathcal{E})$ be a hypergraph with maximum edge size $\\ell$ and maximum degree $\\Delta$. For given numbers $b_v\\in \\mathbb{N}_{\\geq 2}$, $v\\in V$, a set multicover in $\\mathcal{H}$ is a set of edges $C \\subseteq \\mathcal{E}$ such that every vertex $v$ in $V$ belongs to at least $b_v$ edges in $C$. Set Multicover is the problem of finding a minimum-cardinality set multicover. Peleg, Schechtman and Wool conjectured that for any fixed $\\Delta$ and $b:=\\min_{v\\in V}b_{v}$, the problem of \\sbmultcov is not approximable within a ratio less than $\\delta:=\\Delta-b+1$, unless $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06936","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/2003.06936/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"}