{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YSBWW7PWZEDA2Z3XS6DQ35FUBZ","short_pith_number":"pith:YSBWW7PW","schema_version":"1.0","canonical_sha256":"c4836b7df6c9060d677797870df4b40e661fb4506898c3565913ebd02c1f48a1","source":{"kind":"arxiv","id":"1112.0689","version":1},"attestation_state":"computed","paper":{"title":"Approximating Low-Dimensional Coverage Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Ashwinkumar Badanidiyuru, Hooyeon Lee, Robert Kleinberg","submitted_at":"2011-12-03T20:52:31Z","abstract_excerpt":"We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\\eps)$-approximation to the maximum-cardinality union of $k$ sets, in running time $O(f(\\eps,k,d)\\cdot poly(n))$ where $n$ is the problem size, $d$ is the VC-dimension of the set system, and $f(\\eps,k,d)$ is exponential in $(kd/\\eps)^c$ for some constant $c$. We complement this positive result by showing that the function $f(\\eps,k,d)$ in the running-time bound cannot be replaced by a fun"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.0689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-12-03T20:52:31Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"7e636a2ee17f575e8767487362c60b5bf33218e74fbef17d8721713ab9bd4b9c","abstract_canon_sha256":"3eb3edfe0476ac304a6a6a4f114d6d4bd3e1fc274162639bb97beac29e56880c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.929448Z","signature_b64":"c4Kyg6vEw1BDEHdVWve6Oc7tFqMha4rBHAL5URvTY26wGwF9FxYbLwbDehJuTGXtbgMxmhY3PQSHdPQJcKGvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4836b7df6c9060d677797870df4b40e661fb4506898c3565913ebd02c1f48a1","last_reissued_at":"2026-05-18T04:07:05.928700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.928700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating Low-Dimensional Coverage Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Ashwinkumar Badanidiyuru, Hooyeon Lee, Robert Kleinberg","submitted_at":"2011-12-03T20:52:31Z","abstract_excerpt":"We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\\eps)$-approximation to the maximum-cardinality union of $k$ sets, in running time $O(f(\\eps,k,d)\\cdot poly(n))$ where $n$ is the problem size, $d$ is the VC-dimension of the set system, and $f(\\eps,k,d)$ is exponential in $(kd/\\eps)^c$ for some constant $c$. We complement this positive result by showing that the function $f(\\eps,k,d)$ in the running-time bound cannot be replaced by a fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0689","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.0689","created_at":"2026-05-18T04:07:05.928812+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0689v1","created_at":"2026-05-18T04:07:05.928812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0689","created_at":"2026-05-18T04:07:05.928812+00:00"},{"alias_kind":"pith_short_12","alias_value":"YSBWW7PWZEDA","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YSBWW7PWZEDA2Z3X","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YSBWW7PW","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ","json":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ.json","graph_json":"https://pith.science/api/pith-number/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/graph.json","events_json":"https://pith.science/api/pith-number/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/events.json","paper":"https://pith.science/paper/YSBWW7PW"},"agent_actions":{"view_html":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ","download_json":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ.json","view_paper":"https://pith.science/paper/YSBWW7PW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0689&json=true","fetch_graph":"https://pith.science/api/pith-number/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/action/storage_attestation","attest_author":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/action/author_attestation","sign_citation":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/action/citation_signature","submit_replication":"https://pith.science/pith/YSBWW7PWZEDA2Z3XS6DQ35FUBZ/action/replication_record"}},"created_at":"2026-05-18T04:07:05.928812+00:00","updated_at":"2026-05-18T04:07:05.928812+00:00"}