{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JJ6ME47DSTQF23YVAR4Z4WQYDP","short_pith_number":"pith:JJ6ME47D","schema_version":"1.0","canonical_sha256":"4a7cc273e394e05d6f1504799e5a181bc2f6d878313f2e6e4a6ac76adc18266f","source":{"kind":"arxiv","id":"1412.1254","version":3},"attestation_state":"computed","paper":{"title":"Longest Common Extensions in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gad M. Landau, Inge Li Goertz, Oren Weimann, Pawel Gawrychowski, Philip Bille","submitted_at":"2014-12-03T10:02:47Z","abstract_excerpt":"The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In this paper we generalize the LCE problem to trees and suggest a few applications of LCE in trees to tries and XML databases. Given a labeled and rooted tree $T$ of size $n$, the goal is to preprocess $T$ into a compact data structure that support the following LCE queries between subpaths and subtrees in $T$. Let $v_1$, $v_2$, $w_1$, and $w_2$ be"},"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":"1412.1254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-03T10:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"6e8c2e1005cca2fe2a1187c2f6b546f909af5ebd80b938a9f85777e24410a8ce","abstract_canon_sha256":"9943b67729c068f0b289335ebbe67fe5f22c81f5bda1634abcf918d9a4bf72a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:07.668569Z","signature_b64":"Soyg35Fv0CsVUcXukdNJvvJi44CZuIP9ja13PZtaWH2+AV6Ex0jiLdBpFedfHmxb6yKQ6VTlD9ukM7TIX2t7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a7cc273e394e05d6f1504799e5a181bc2f6d878313f2e6e4a6ac76adc18266f","last_reissued_at":"2026-05-18T01:37:07.668000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:07.668000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Longest Common Extensions in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gad M. Landau, Inge Li Goertz, Oren Weimann, Pawel Gawrychowski, Philip Bille","submitted_at":"2014-12-03T10:02:47Z","abstract_excerpt":"The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE queries. In this paper we generalize the LCE problem to trees and suggest a few applications of LCE in trees to tries and XML databases. Given a labeled and rooted tree $T$ of size $n$, the goal is to preprocess $T$ into a compact data structure that support the following LCE queries between subpaths and subtrees in $T$. Let $v_1$, $v_2$, $w_1$, and $w_2$ be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1254","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":"1412.1254","created_at":"2026-05-18T01:37:07.668078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1254v3","created_at":"2026-05-18T01:37:07.668078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1254","created_at":"2026-05-18T01:37:07.668078+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJ6ME47DSTQF","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJ6ME47DSTQF23YV","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJ6ME47D","created_at":"2026-05-18T12:28:33.132498+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/JJ6ME47DSTQF23YVAR4Z4WQYDP","json":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP.json","graph_json":"https://pith.science/api/pith-number/JJ6ME47DSTQF23YVAR4Z4WQYDP/graph.json","events_json":"https://pith.science/api/pith-number/JJ6ME47DSTQF23YVAR4Z4WQYDP/events.json","paper":"https://pith.science/paper/JJ6ME47D"},"agent_actions":{"view_html":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP","download_json":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP.json","view_paper":"https://pith.science/paper/JJ6ME47D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1254&json=true","fetch_graph":"https://pith.science/api/pith-number/JJ6ME47DSTQF23YVAR4Z4WQYDP/graph.json","fetch_events":"https://pith.science/api/pith-number/JJ6ME47DSTQF23YVAR4Z4WQYDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP/action/storage_attestation","attest_author":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP/action/author_attestation","sign_citation":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP/action/citation_signature","submit_replication":"https://pith.science/pith/JJ6ME47DSTQF23YVAR4Z4WQYDP/action/replication_record"}},"created_at":"2026-05-18T01:37:07.668078+00:00","updated_at":"2026-05-18T01:37:07.668078+00:00"}