{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LNNG3ACJ3ISFSFJ4XQKABVCOBK","short_pith_number":"pith:LNNG3ACJ","schema_version":"1.0","canonical_sha256":"5b5a6d8049da2459153cbc1400d44e0a806af1ee6d12129d50ff1b208c912531","source":{"kind":"arxiv","id":"1504.06647","version":2},"attestation_state":"computed","paper":{"title":"Approximating LZ77 via Small-Space Multiple-Pattern Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Johannes Fischer, Pawe{\\l} Gawrychowski, Tomasz Kociumaka, Travis Gagie","submitted_at":"2015-04-24T21:26:58Z","abstract_excerpt":"We generalize Karp-Rabin string matching to handle multiple patterns in $\\mathcal{O}(n \\log n + m)$ time and $\\mathcal{O}(s)$ space, where $n$ is the length of the text and $m$ is the total length of the $s$ patterns, returning correct answers with high probability. As a prime application of our algorithm, we show how to approximate the LZ77 parse of a string of length $n$. If the optimal parse consists of $z$ phrases, using only $\\mathcal{O}(z)$ working space we can return a parse consisting of at most $(1+\\varepsilon)z$ phrases in $\\mathcal{O}(\\varepsilon^{-1}n\\log n)$ time, for any $\\vareps"},"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":"1504.06647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-24T21:26:58Z","cross_cats_sorted":[],"title_canon_sha256":"11e7b635548463236e48e0097f24437709cfc0f8aad67b5d39595eb0f15162ab","abstract_canon_sha256":"5fd3dd7ca9fd16ad44c853bcf0c49a6c4d7a66ba06ed9f9ff652594a7004a7c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:32.173103Z","signature_b64":"8344uUZfjfT5JWvrswLH4bOq5J1S3H5eRmkrCN5N9BNBEVnyK5xPJqcYiHdK957CcpXLWe64pyesQOBztVh/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5a6d8049da2459153cbc1400d44e0a806af1ee6d12129d50ff1b208c912531","last_reissued_at":"2026-05-18T01:33:32.172379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:32.172379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximating LZ77 via Small-Space Multiple-Pattern Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Johannes Fischer, Pawe{\\l} Gawrychowski, Tomasz Kociumaka, Travis Gagie","submitted_at":"2015-04-24T21:26:58Z","abstract_excerpt":"We generalize Karp-Rabin string matching to handle multiple patterns in $\\mathcal{O}(n \\log n + m)$ time and $\\mathcal{O}(s)$ space, where $n$ is the length of the text and $m$ is the total length of the $s$ patterns, returning correct answers with high probability. As a prime application of our algorithm, we show how to approximate the LZ77 parse of a string of length $n$. If the optimal parse consists of $z$ phrases, using only $\\mathcal{O}(z)$ working space we can return a parse consisting of at most $(1+\\varepsilon)z$ phrases in $\\mathcal{O}(\\varepsilon^{-1}n\\log n)$ time, for any $\\vareps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06647","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":"1504.06647","created_at":"2026-05-18T01:33:32.172491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06647v2","created_at":"2026-05-18T01:33:32.172491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06647","created_at":"2026-05-18T01:33:32.172491+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNNG3ACJ3ISF","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNNG3ACJ3ISFSFJ4","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNNG3ACJ","created_at":"2026-05-18T12:29:29.992203+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/LNNG3ACJ3ISFSFJ4XQKABVCOBK","json":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK.json","graph_json":"https://pith.science/api/pith-number/LNNG3ACJ3ISFSFJ4XQKABVCOBK/graph.json","events_json":"https://pith.science/api/pith-number/LNNG3ACJ3ISFSFJ4XQKABVCOBK/events.json","paper":"https://pith.science/paper/LNNG3ACJ"},"agent_actions":{"view_html":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK","download_json":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK.json","view_paper":"https://pith.science/paper/LNNG3ACJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06647&json=true","fetch_graph":"https://pith.science/api/pith-number/LNNG3ACJ3ISFSFJ4XQKABVCOBK/graph.json","fetch_events":"https://pith.science/api/pith-number/LNNG3ACJ3ISFSFJ4XQKABVCOBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK/action/storage_attestation","attest_author":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK/action/author_attestation","sign_citation":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK/action/citation_signature","submit_replication":"https://pith.science/pith/LNNG3ACJ3ISFSFJ4XQKABVCOBK/action/replication_record"}},"created_at":"2026-05-18T01:33:32.172491+00:00","updated_at":"2026-05-18T01:33:32.172491+00:00"}