{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:62DAKKGTJWYCUCGR4CX7FTGRFG","short_pith_number":"pith:62DAKKGT","schema_version":"1.0","canonical_sha256":"f6860528d34db02a08d1e0aff2ccd129b874f489d013f1ecd99865499d464bcc","source":{"kind":"arxiv","id":"1502.07663","version":3},"attestation_state":"computed","paper":{"title":"Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Pawel Gawrychowski, Shay Mozes","submitted_at":"2015-02-26T18:22:03Z","abstract_excerpt":"We present an optimal data structure for submatrix maximum queries in n x n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(loglogn) time. It also gives a matching lower bound, showing that O(loglogn) query-time is optimal for any data structure of size O(n polylog(n)). Our result concludes a line of improvements that started in SODA'12 with O(log^2 n) query-time and continued in ICALP'14 with O(log"},"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":"1502.07663","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-02-26T18:22:03Z","cross_cats_sorted":[],"title_canon_sha256":"e7baee17fec951fc181677c3ccc9d89a86797a7179c782a385f4d104adc3933c","abstract_canon_sha256":"4ef2dfa15d7a172576e66fea264bb7d2e4975ca2ec2f02b13d107ec9b9a31c69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:22.636128Z","signature_b64":"2BaKTzf5YOiV3jXjMmlQ2wFaMjQjW7LP/6OfcjE5xNfYUYynycP/VDz1ITRW30G4ruyN9g6GWx1mPpGnfwoACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6860528d34db02a08d1e0aff2ccd129b874f489d013f1ecd99865499d464bcc","last_reissued_at":"2026-05-18T00:27:22.635346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:22.635346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Pawel Gawrychowski, Shay Mozes","submitted_at":"2015-02-26T18:22:03Z","abstract_excerpt":"We present an optimal data structure for submatrix maximum queries in n x n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(loglogn) time. It also gives a matching lower bound, showing that O(loglogn) query-time is optimal for any data structure of size O(n polylog(n)). Our result concludes a line of improvements that started in SODA'12 with O(log^2 n) query-time and continued in ICALP'14 with O(log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07663","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.07663","created_at":"2026-05-18T00:27:22.635463+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.07663v3","created_at":"2026-05-18T00:27:22.635463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07663","created_at":"2026-05-18T00:27:22.635463+00:00"},{"alias_kind":"pith_short_12","alias_value":"62DAKKGTJWYC","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"62DAKKGTJWYCUCGR","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"62DAKKGT","created_at":"2026-05-18T12:29:07.941421+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/62DAKKGTJWYCUCGR4CX7FTGRFG","json":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG.json","graph_json":"https://pith.science/api/pith-number/62DAKKGTJWYCUCGR4CX7FTGRFG/graph.json","events_json":"https://pith.science/api/pith-number/62DAKKGTJWYCUCGR4CX7FTGRFG/events.json","paper":"https://pith.science/paper/62DAKKGT"},"agent_actions":{"view_html":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG","download_json":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG.json","view_paper":"https://pith.science/paper/62DAKKGT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.07663&json=true","fetch_graph":"https://pith.science/api/pith-number/62DAKKGTJWYCUCGR4CX7FTGRFG/graph.json","fetch_events":"https://pith.science/api/pith-number/62DAKKGTJWYCUCGR4CX7FTGRFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG/action/storage_attestation","attest_author":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG/action/author_attestation","sign_citation":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG/action/citation_signature","submit_replication":"https://pith.science/pith/62DAKKGTJWYCUCGR4CX7FTGRFG/action/replication_record"}},"created_at":"2026-05-18T00:27:22.635463+00:00","updated_at":"2026-05-18T00:27:22.635463+00:00"}