{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LCXTPQ2LE2X7U4W4I67ORI3C27","short_pith_number":"pith:LCXTPQ2L","schema_version":"1.0","canonical_sha256":"58af37c34b26affa72dc47bee8a362d7dd22e41019051c5c5ece540fbc5aaa23","source":{"kind":"arxiv","id":"1512.00481","version":2},"attestation_state":"computed","paper":{"title":"Hitting Set for hypergraphs of low VC-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, L\\'aszl\\'o Kozma, N.S. Narayanaswamy, Shay Moran","submitted_at":"2015-12-01T21:07:51Z","abstract_excerpt":"We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis dimension (VC-dimension) of the input is small. VC-dimension is a natural measure of complexity of set systems. Several tractable instances of Hitting Set with a geometric or graph-theoretical flavor are known to have low VC-dimension. In set systems of bounded VC-dimension, Hitting Set is known to admit efficient and almost optimal approximation algorithms (Br\\\"on"},"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":"1512.00481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-01T21:07:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"82a07a04bf7e91dd6b9a5c8b4d7a01dd33d8497388d5a528d05ba5c7939025a7","abstract_canon_sha256":"7595f8b7198e82bad347c33346cedf6160f7d39aace83e6016b0a74ab0617d32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:12.794903Z","signature_b64":"MrdaX1Rb9PYD6qx/mILb2Jaxgv2me9+KXp2Cb6NQnnWp4hP89UqFglqLUBfFWJsssLAsXui5jb1sCI3Luq9XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58af37c34b26affa72dc47bee8a362d7dd22e41019051c5c5ece540fbc5aaa23","last_reissued_at":"2026-05-18T01:12:12.794290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:12.794290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hitting Set for hypergraphs of low VC-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Karl Bringmann, L\\'aszl\\'o Kozma, N.S. Narayanaswamy, Shay Moran","submitted_at":"2015-12-01T21:07:51Z","abstract_excerpt":"We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis dimension (VC-dimension) of the input is small. VC-dimension is a natural measure of complexity of set systems. Several tractable instances of Hitting Set with a geometric or graph-theoretical flavor are known to have low VC-dimension. In set systems of bounded VC-dimension, Hitting Set is known to admit efficient and almost optimal approximation algorithms (Br\\\"on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00481","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.00481","created_at":"2026-05-18T01:12:12.794388+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00481v2","created_at":"2026-05-18T01:12:12.794388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00481","created_at":"2026-05-18T01:12:12.794388+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCXTPQ2LE2X7","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCXTPQ2LE2X7U4W4","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCXTPQ2L","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.11873","citing_title":"Maximizing Reachability via Shifting of Temporal Paths","ref_index":156,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27","json":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27.json","graph_json":"https://pith.science/api/pith-number/LCXTPQ2LE2X7U4W4I67ORI3C27/graph.json","events_json":"https://pith.science/api/pith-number/LCXTPQ2LE2X7U4W4I67ORI3C27/events.json","paper":"https://pith.science/paper/LCXTPQ2L"},"agent_actions":{"view_html":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27","download_json":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27.json","view_paper":"https://pith.science/paper/LCXTPQ2L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00481&json=true","fetch_graph":"https://pith.science/api/pith-number/LCXTPQ2LE2X7U4W4I67ORI3C27/graph.json","fetch_events":"https://pith.science/api/pith-number/LCXTPQ2LE2X7U4W4I67ORI3C27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27/action/storage_attestation","attest_author":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27/action/author_attestation","sign_citation":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27/action/citation_signature","submit_replication":"https://pith.science/pith/LCXTPQ2LE2X7U4W4I67ORI3C27/action/replication_record"}},"created_at":"2026-05-18T01:12:12.794388+00:00","updated_at":"2026-05-18T01:12:12.794388+00:00"}