{"paper":{"title":"No O(N) queries for checking if N intervals cover everything or for piercing N pairs of intervals. An O(N log N)-steps algorithm for piercing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.MG"],"primary_cat":"math.CO","authors_text":"Eliahu Levy, Meir Katchalski","submitted_at":"2011-09-13T12:50:26Z","abstract_excerpt":"The complexity of two related geometrical (indeed, combinatorial) problems is considered, measured by the number of queries needed to determine the solution. It is proved that one cannot check in a linear in N number of queries whether N intervals cover a whole interval, or whether for N pairs of intervals on two lines there is a pair of points intersecting each of these pairs of intervals (\"piercing all pairs of intervals\"). The proofs are related to examples which show that there is no \"Helly property\" here - the whole set of N may cover the whole interval (resp. may have no pair of points p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2763","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":""},"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"}