{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TA5UZD452JBRNUPXEFT6ZAI4HU","short_pith_number":"pith:TA5UZD45","schema_version":"1.0","canonical_sha256":"983b4c8f9dd24316d1f72167ec811c3d1cf68cbdca6ac05154f96d2af74d85cb","source":{"kind":"arxiv","id":"1805.11170","version":2},"attestation_state":"computed","paper":{"title":"Strongly polynomial efficient approximation scheme for segmentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.DS","authors_text":"Nikolaj Tatti","submitted_at":"2018-05-28T20:55:47Z","abstract_excerpt":"Partitioning a sequence of length $n$ into $k$ coherent segments (Seg) is one of the classic optimization problems. As long as the optimization criterion is additive, Seg can be solved exactly in $O(n^2k)$ time using a classic dynamic program. Due to the quadratic term, computing the exact segmentation may be too expensive for long sequences, which has led to development of approximate solutions. We consider an existing estimation scheme that computes $(1 + \\epsilon)$ approximation in polylogarithmic time. We augment this algorithm, making it strongly polynomial. We do this by first solving a "},"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":"1805.11170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-28T20:55:47Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"2b217ebc1262a05c11deebb827750716c3ac54f67a38321f79819207db343be9","abstract_canon_sha256":"9288b50438583fda4bf2f7b0cce60770f4932e023abdb7e33bc8bc3ae61e6e4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:48.388778Z","signature_b64":"hWNDHYsF8MyuKI0hJVOgRTvheXHsjlyS2owOyZNV0TW+nWlmjFLGuInywHLIbyPpy2wxaMUpfcbW/hnhHdtfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"983b4c8f9dd24316d1f72167ec811c3d1cf68cbdca6ac05154f96d2af74d85cb","last_reissued_at":"2026-05-17T23:54:48.388203Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:48.388203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly polynomial efficient approximation scheme for segmentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.DS","authors_text":"Nikolaj Tatti","submitted_at":"2018-05-28T20:55:47Z","abstract_excerpt":"Partitioning a sequence of length $n$ into $k$ coherent segments (Seg) is one of the classic optimization problems. As long as the optimization criterion is additive, Seg can be solved exactly in $O(n^2k)$ time using a classic dynamic program. Due to the quadratic term, computing the exact segmentation may be too expensive for long sequences, which has led to development of approximate solutions. We consider an existing estimation scheme that computes $(1 + \\epsilon)$ approximation in polylogarithmic time. We augment this algorithm, making it strongly polynomial. We do this by first solving a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11170","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":"1805.11170","created_at":"2026-05-17T23:54:48.388306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.11170v2","created_at":"2026-05-17T23:54:48.388306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11170","created_at":"2026-05-17T23:54:48.388306+00:00"},{"alias_kind":"pith_short_12","alias_value":"TA5UZD452JBR","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TA5UZD452JBRNUPX","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TA5UZD45","created_at":"2026-05-18T12:32:53.628368+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/TA5UZD452JBRNUPXEFT6ZAI4HU","json":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU.json","graph_json":"https://pith.science/api/pith-number/TA5UZD452JBRNUPXEFT6ZAI4HU/graph.json","events_json":"https://pith.science/api/pith-number/TA5UZD452JBRNUPXEFT6ZAI4HU/events.json","paper":"https://pith.science/paper/TA5UZD45"},"agent_actions":{"view_html":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU","download_json":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU.json","view_paper":"https://pith.science/paper/TA5UZD45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.11170&json=true","fetch_graph":"https://pith.science/api/pith-number/TA5UZD452JBRNUPXEFT6ZAI4HU/graph.json","fetch_events":"https://pith.science/api/pith-number/TA5UZD452JBRNUPXEFT6ZAI4HU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU/action/storage_attestation","attest_author":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU/action/author_attestation","sign_citation":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU/action/citation_signature","submit_replication":"https://pith.science/pith/TA5UZD452JBRNUPXEFT6ZAI4HU/action/replication_record"}},"created_at":"2026-05-17T23:54:48.388306+00:00","updated_at":"2026-05-17T23:54:48.388306+00:00"}