{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PPTNORK7AH53TJVMY3WNCQQOCF","short_pith_number":"pith:PPTNORK7","schema_version":"1.0","canonical_sha256":"7be6d7455f01fbb9a6acc6ecd1420e1155c64c81a8c23f4faf1c37a8bea32148","source":{"kind":"arxiv","id":"1203.4900","version":1},"attestation_state":"computed","paper":{"title":"Single pass sparsification in the streaming model with edge deletions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ashish Goel, Ian Post, Michael Kapralov","submitted_at":"2012-03-22T07:45:13Z","abstract_excerpt":"In this paper we give a construction of cut sparsifiers of Benczur and Karger in the {\\em dynamic} streaming setting in a single pass over the data stream. Previous constructions either required multiple passes or were unable to handle edge deletions. We use $\\tilde{O}(1/\\e^2)$ time for each stream update and $\\tilde{O}(n/\\e^2)$ time to construct a sparsifier. Our $\\e$-sparsifiers have $O(n\\log^3 n/\\e^2)$ edges. The main tools behind our result are an application of sketching techniques of Ahn et al.[SODA'12] to estimate edge connectivity together with a novel application of sampling with limi"},"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":"1203.4900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-03-22T07:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"5353974959d72d78bf00eb8db6f91909a84ebb134650ee8422c11c72f5037a32","abstract_canon_sha256":"58f4f65c44f1d2bba342318baa153fd8a0375dc4a16e19caf8e38064072edb7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:28.436185Z","signature_b64":"xkQuRNiiLXmOb/JvzZmMXmHcch+CFF8K0DU2ldWiWOhvoZWbP+P+NEsVmP0SuHD9oTRrXE89wHME0dkHAggwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be6d7455f01fbb9a6acc6ecd1420e1155c64c81a8c23f4faf1c37a8bea32148","last_reissued_at":"2026-05-18T03:59:28.435648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:28.435648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Single pass sparsification in the streaming model with edge deletions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ashish Goel, Ian Post, Michael Kapralov","submitted_at":"2012-03-22T07:45:13Z","abstract_excerpt":"In this paper we give a construction of cut sparsifiers of Benczur and Karger in the {\\em dynamic} streaming setting in a single pass over the data stream. Previous constructions either required multiple passes or were unable to handle edge deletions. We use $\\tilde{O}(1/\\e^2)$ time for each stream update and $\\tilde{O}(n/\\e^2)$ time to construct a sparsifier. Our $\\e$-sparsifiers have $O(n\\log^3 n/\\e^2)$ edges. The main tools behind our result are an application of sketching techniques of Ahn et al.[SODA'12] to estimate edge connectivity together with a novel application of sampling with limi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4900","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":"1203.4900","created_at":"2026-05-18T03:59:28.435709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.4900v1","created_at":"2026-05-18T03:59:28.435709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4900","created_at":"2026-05-18T03:59:28.435709+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPTNORK7AH53","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPTNORK7AH53TJVM","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPTNORK7","created_at":"2026-05-18T12:27:18.751474+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/PPTNORK7AH53TJVMY3WNCQQOCF","json":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF.json","graph_json":"https://pith.science/api/pith-number/PPTNORK7AH53TJVMY3WNCQQOCF/graph.json","events_json":"https://pith.science/api/pith-number/PPTNORK7AH53TJVMY3WNCQQOCF/events.json","paper":"https://pith.science/paper/PPTNORK7"},"agent_actions":{"view_html":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF","download_json":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF.json","view_paper":"https://pith.science/paper/PPTNORK7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.4900&json=true","fetch_graph":"https://pith.science/api/pith-number/PPTNORK7AH53TJVMY3WNCQQOCF/graph.json","fetch_events":"https://pith.science/api/pith-number/PPTNORK7AH53TJVMY3WNCQQOCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF/action/storage_attestation","attest_author":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF/action/author_attestation","sign_citation":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF/action/citation_signature","submit_replication":"https://pith.science/pith/PPTNORK7AH53TJVMY3WNCQQOCF/action/replication_record"}},"created_at":"2026-05-18T03:59:28.435709+00:00","updated_at":"2026-05-18T03:59:28.435709+00:00"}