{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NFE2VWCYLGCPWCUQU6TTH6RIQU","short_pith_number":"pith:NFE2VWCY","schema_version":"1.0","canonical_sha256":"6949aad8585984fb0a90a7a733fa28850309adaaa52f2a366044b1296d47580c","source":{"kind":"arxiv","id":"1507.07080","version":1},"attestation_state":"computed","paper":{"title":"Range Predecessor and Lempel-Ziv Parsing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Simon J. Puglisi","submitted_at":"2015-07-25T08:42:56Z","abstract_excerpt":"The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the Lempel-Ziv parsing of a string of length $n$ on an alphabet of size $\\sigma$ can be computed in $O(n\\log\\log\\sigma)$ time ($O(n)$ time if we allow randomization) using $O(n\\log\\sigma)$ bits of working space; that is, using space proportional to that of the input string in bits. The previous fastest algorithm using $O(n\\log\\sigma)$ space takes $O(n(\\log\\sigma+\\log\\log n))$ time. We also consider the important rightmost var"},"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":"1507.07080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-25T08:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"9a135a35b44162d5b43edaae245bb05e8650de7900dbddbad7d046d4980425cb","abstract_canon_sha256":"11abdcd5765d8ace10110daf32bdb8ca377167f2ac6c3170827a83629fcead48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:17.267518Z","signature_b64":"IcVEy6ODU8bagn2CW/2VEXz5/MYeghZ3DJMG/ox3UuWgslQq94ENFzyTsl670jxjwSIIcVAwBZCVVTeh/UhwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6949aad8585984fb0a90a7a733fa28850309adaaa52f2a366044b1296d47580c","last_reissued_at":"2026-05-18T01:36:17.266911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:17.266911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Range Predecessor and Lempel-Ziv Parsing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Simon J. Puglisi","submitted_at":"2015-07-25T08:42:56Z","abstract_excerpt":"The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the Lempel-Ziv parsing of a string of length $n$ on an alphabet of size $\\sigma$ can be computed in $O(n\\log\\log\\sigma)$ time ($O(n)$ time if we allow randomization) using $O(n\\log\\sigma)$ bits of working space; that is, using space proportional to that of the input string in bits. The previous fastest algorithm using $O(n\\log\\sigma)$ space takes $O(n(\\log\\sigma+\\log\\log n))$ time. We also consider the important rightmost var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07080","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":"1507.07080","created_at":"2026-05-18T01:36:17.266989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07080v1","created_at":"2026-05-18T01:36:17.266989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07080","created_at":"2026-05-18T01:36:17.266989+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFE2VWCYLGCP","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFE2VWCYLGCPWCUQ","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFE2VWCY","created_at":"2026-05-18T12:29:32.376354+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/NFE2VWCYLGCPWCUQU6TTH6RIQU","json":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU.json","graph_json":"https://pith.science/api/pith-number/NFE2VWCYLGCPWCUQU6TTH6RIQU/graph.json","events_json":"https://pith.science/api/pith-number/NFE2VWCYLGCPWCUQU6TTH6RIQU/events.json","paper":"https://pith.science/paper/NFE2VWCY"},"agent_actions":{"view_html":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU","download_json":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU.json","view_paper":"https://pith.science/paper/NFE2VWCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07080&json=true","fetch_graph":"https://pith.science/api/pith-number/NFE2VWCYLGCPWCUQU6TTH6RIQU/graph.json","fetch_events":"https://pith.science/api/pith-number/NFE2VWCYLGCPWCUQU6TTH6RIQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU/action/storage_attestation","attest_author":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU/action/author_attestation","sign_citation":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU/action/citation_signature","submit_replication":"https://pith.science/pith/NFE2VWCYLGCPWCUQU6TTH6RIQU/action/replication_record"}},"created_at":"2026-05-18T01:36:17.266989+00:00","updated_at":"2026-05-18T01:36:17.266989+00:00"}