{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5BWXU2ZZC6JLCI3HPMT5GSKAJB","short_pith_number":"pith:5BWXU2ZZ","schema_version":"1.0","canonical_sha256":"e86d7a6b391792b123677b27d34940485692af3becdc623dd6152766faa583a6","source":{"kind":"arxiv","id":"1607.04200","version":1},"attestation_state":"computed","paper":{"title":"Edit Distance: Sketching, Streaming and Document Exchange","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Qin Zhang","submitted_at":"2016-07-14T16:38:17Z","abstract_excerpt":"We show that in the document exchange problem, where Alice holds $x \\in \\{0,1\\}^n$ and Bob holds $y \\in \\{0,1\\}^n$, Alice can send Bob a message of size $O(K(\\log^2 K+\\log n))$ bits such that Bob can recover $x$ using the message and his input $y$ if the edit distance between $x$ and $y$ is no more than $K$, and output \"error\" otherwise. Both the encoding and decoding can be done in time $\\tilde{O}(n+\\mathsf{poly}(K))$. This result significantly improves the previous communication bounds under polynomial encoding/decoding time. We also show that in the referee model, where Alice and Bob hold $"},"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":"1607.04200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-14T16:38:17Z","cross_cats_sorted":[],"title_canon_sha256":"41545547d70d2e64ed8e3638cd92e275fe2960e75940d03e51ca45c48745df45","abstract_canon_sha256":"6449118edea677f3c04fa0db81860a2971fa8808ef17a93a62a970b604ab2e78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:03.901403Z","signature_b64":"NMZVypcKaSIonS+cC7dP25DHNXd1TbqGaG8E/q0OEV58VU1pCUHOTX/C4he1iX3sX7fCNGXnW1fC5CQf7xAvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e86d7a6b391792b123677b27d34940485692af3becdc623dd6152766faa583a6","last_reissued_at":"2026-05-18T01:11:03.900886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:03.900886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edit Distance: Sketching, Streaming and Document Exchange","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Qin Zhang","submitted_at":"2016-07-14T16:38:17Z","abstract_excerpt":"We show that in the document exchange problem, where Alice holds $x \\in \\{0,1\\}^n$ and Bob holds $y \\in \\{0,1\\}^n$, Alice can send Bob a message of size $O(K(\\log^2 K+\\log n))$ bits such that Bob can recover $x$ using the message and his input $y$ if the edit distance between $x$ and $y$ is no more than $K$, and output \"error\" otherwise. Both the encoding and decoding can be done in time $\\tilde{O}(n+\\mathsf{poly}(K))$. This result significantly improves the previous communication bounds under polynomial encoding/decoding time. We also show that in the referee model, where Alice and Bob hold $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04200","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":"1607.04200","created_at":"2026-05-18T01:11:03.900953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04200v1","created_at":"2026-05-18T01:11:03.900953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04200","created_at":"2026-05-18T01:11:03.900953+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BWXU2ZZC6JL","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BWXU2ZZC6JLCI3H","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BWXU2ZZ","created_at":"2026-05-18T12:29:58.707656+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/5BWXU2ZZC6JLCI3HPMT5GSKAJB","json":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB.json","graph_json":"https://pith.science/api/pith-number/5BWXU2ZZC6JLCI3HPMT5GSKAJB/graph.json","events_json":"https://pith.science/api/pith-number/5BWXU2ZZC6JLCI3HPMT5GSKAJB/events.json","paper":"https://pith.science/paper/5BWXU2ZZ"},"agent_actions":{"view_html":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB","download_json":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB.json","view_paper":"https://pith.science/paper/5BWXU2ZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04200&json=true","fetch_graph":"https://pith.science/api/pith-number/5BWXU2ZZC6JLCI3HPMT5GSKAJB/graph.json","fetch_events":"https://pith.science/api/pith-number/5BWXU2ZZC6JLCI3HPMT5GSKAJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB/action/storage_attestation","attest_author":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB/action/author_attestation","sign_citation":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB/action/citation_signature","submit_replication":"https://pith.science/pith/5BWXU2ZZC6JLCI3HPMT5GSKAJB/action/replication_record"}},"created_at":"2026-05-18T01:11:03.900953+00:00","updated_at":"2026-05-18T01:11:03.900953+00:00"}