{"paper":{"title":"Density Functions subject to a Co-Matroid Constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Natwar Modani, Sambuddha Roy, Sivaramakrishnan R. Natarajan, Venkatesan T. Chakaravarthy, Yogish Sabharwal","submitted_at":"2012-07-22T11:01:33Z","abstract_excerpt":"In this paper we consider the problem of finding the {\\em densest} subset subject to {\\em co-matroid constraints}. We are given a {\\em monotone supermodular} set function $f$ defined over a universe $U$, and the density of a subset $S$ is defined to be $f(S)/\\crd{S}$. This generalizes the concept of graph density. Co-matroid constraints are the following: given matroid $\\calM$ a set $S$ is feasible, iff the complement of $S$ is {\\em independent} in the matroid. Under such constraints, the problem becomes $\\np$-hard. The specific case of graph density has been considered in literature under spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5215","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}