{"paper":{"title":"Computing Coverage Kernels Under Restricted Settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Javiel Rojas-Ledesma, J\\'er\\'emy Barbay, Pablo P\\'erez-Lantero","submitted_at":"2018-05-11T02:08:49Z","abstract_excerpt":"We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\\mathsf{NP}$-hard, but as for many $\\mathsf{NP}$-hard problems on graphs, the problem becomes solvable in polynomial time under restrictions on the graph induced by $B$. We consider various classes of graphs, show that Minimum Coverage Kernel remains $\\mathsf{NP}$-hard even for severely restricted instances, and provide two polynomial time approximation algorithms for this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04223","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"}