{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XMDBY7HULAHU5RPTLRKUAZY6LX","short_pith_number":"pith:XMDBY7HU","schema_version":"1.0","canonical_sha256":"bb061c7cf4580f4ec5f35c5540671e5dc2a2004ada483365b18c0eeb532bae39","source":{"kind":"arxiv","id":"1510.04590","version":1},"attestation_state":"computed","paper":{"title":"An Improved Randomized Data Structure for Dynamic Graph Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Zhengyu Wang","submitted_at":"2015-10-15T15:41:36Z","abstract_excerpt":"We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\\log^3 n)$ per edge insertion, $O(\\log^4 n)$ per edge deletion, and $O(\\log n/\\log\\log n)$ per query, where $n$ is the number of vertices. The previous best algorithm has worst case running time $O(\\log^4 n)$ per edge insertion and $O(\\log^5 n)$ per edge deletion. The improvement is made by reducing the randomness used in the previous result, so that we save a $\\log n$ factor in update time.\n  Specifically, \\c"},"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":"1510.04590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T15:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"d7b24a93a57518170da5e55ed3679c1ea5abb55c50893dfb0355ce8f4e935e68","abstract_canon_sha256":"659c5202b41e63993844ebd9dad149b73ac17864c684983c59c1ea349cfba891"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:02.189632Z","signature_b64":"Us3+IEYH7d3Hq3igMtgETlYuboKZujs8fRokHMzlKjtfz9EyARRbDCNrLQ1ZsZ6H41ayWGjGFC61nFsK2p5xAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb061c7cf4580f4ec5f35c5540671e5dc2a2004ada483365b18c0eeb532bae39","last_reissued_at":"2026-05-18T01:30:02.188911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:02.188911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Improved Randomized Data Structure for Dynamic Graph Connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Zhengyu Wang","submitted_at":"2015-10-15T15:41:36Z","abstract_excerpt":"We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\\log^3 n)$ per edge insertion, $O(\\log^4 n)$ per edge deletion, and $O(\\log n/\\log\\log n)$ per query, where $n$ is the number of vertices. The previous best algorithm has worst case running time $O(\\log^4 n)$ per edge insertion and $O(\\log^5 n)$ per edge deletion. The improvement is made by reducing the randomness used in the previous result, so that we save a $\\log n$ factor in update time.\n  Specifically, \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04590","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":"1510.04590","created_at":"2026-05-18T01:30:02.189040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04590v1","created_at":"2026-05-18T01:30:02.189040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04590","created_at":"2026-05-18T01:30:02.189040+00:00"},{"alias_kind":"pith_short_12","alias_value":"XMDBY7HULAHU","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XMDBY7HULAHU5RPT","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XMDBY7HU","created_at":"2026-05-18T12:29:50.041715+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/XMDBY7HULAHU5RPTLRKUAZY6LX","json":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX.json","graph_json":"https://pith.science/api/pith-number/XMDBY7HULAHU5RPTLRKUAZY6LX/graph.json","events_json":"https://pith.science/api/pith-number/XMDBY7HULAHU5RPTLRKUAZY6LX/events.json","paper":"https://pith.science/paper/XMDBY7HU"},"agent_actions":{"view_html":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX","download_json":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX.json","view_paper":"https://pith.science/paper/XMDBY7HU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04590&json=true","fetch_graph":"https://pith.science/api/pith-number/XMDBY7HULAHU5RPTLRKUAZY6LX/graph.json","fetch_events":"https://pith.science/api/pith-number/XMDBY7HULAHU5RPTLRKUAZY6LX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX/action/storage_attestation","attest_author":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX/action/author_attestation","sign_citation":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX/action/citation_signature","submit_replication":"https://pith.science/pith/XMDBY7HULAHU5RPTLRKUAZY6LX/action/replication_record"}},"created_at":"2026-05-18T01:30:02.189040+00:00","updated_at":"2026-05-18T01:30:02.189040+00:00"}