{"paper":{"title":"Tight Approximation Guarantees for Concave Coverage Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Omar Fawzi, Paul Ferm\\'e, Siddharth Barman","submitted_at":"2020-10-02T13:03:04Z","abstract_excerpt":"In the maximum coverage problem, we are given subsets $T_1, \\ldots, T_m$ of a universe $[n]$ along with an integer $k$ and the objective is to find a subset $S \\subseteq [m]$ of size $k$ that maximizes $C(S) := \\Big|\\bigcup_{i \\in S} T_i\\Big|$. It is a classic result that the greedy algorithm for this problem achieves an optimal approximation ratio of $1-e^{-1}$.\n  In this work we consider a generalization of this problem wherein an element $a$ can contribute by an amount that depends on the number of times it is covered. Given a concave, nondecreasing function $\\varphi$, we define $C^{\\varphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00970","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/2010.00970/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"}