{"paper":{"title":"Kernelization Algorithms for Packing Problems Allowing Overlaps (Extended Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alejandro L\\'opez-Ortiz, Henning Fernau, Jazm\\'in Romero","submitted_at":"2014-11-25T16:47:42Z","abstract_excerpt":"We consider the problem of discovering overlapping communities in networks which we model as generalizations of Graph Packing problems with overlap.\n  We seek a collection $\\mathcal{S}' \\subseteq \\mathcal{S}$ consisting of at least $k$ sets subject to certain disjointness restrictions. In the $r$-Set Packing with $t$-Membership, each element of $\\mathcal{U}$ belongs to at most $t$ sets of $\\mathcal{S'}$ while in $t$-Overlap each pair of sets in $\\mathcal{S'}$ overlaps in at most $t$ elements. Each set of $\\mathcal{S}$ has at most $r$ elements.\n  Similarly, both of our graph packing problems se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6915","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":""},"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"}