{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ST6JGB4WNSUU7PFF6QKKYR5GHC","short_pith_number":"pith:ST6JGB4W","schema_version":"1.0","canonical_sha256":"94fc9307966ca94fbca5f414ac47a6388747233e251fdf6fe7c143113890abdd","source":{"kind":"arxiv","id":"1506.04505","version":3},"attestation_state":"computed","paper":{"title":"Applications of Uniform Sampling: Densest Subgraph and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Hossein Esfandiari, MohammadTaghi Hajiaghayi","submitted_at":"2015-06-15T08:08:55Z","abstract_excerpt":"Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a $(0.5-\\epsilon)$-approximation algorithm using $\\tilde{O}(n)$ space, where factors of $\\epsilon$ and $\\log(n)$ are suppressed in the $\\tilde{O}$ notation. However, the update time of this algorithm is large. To remedy this, they also provide a $(0.25-\\epsilon)$-approximation algorithm using $\\tilde{O}(n)$ space with update time $\\tilde{O}(1)$.\n  In this paper we improv"},"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":"1506.04505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-15T08:08:55Z","cross_cats_sorted":[],"title_canon_sha256":"190454a8029d5144c1a4be97426b8458e062c8208d498aafc6cc9f25511956ee","abstract_canon_sha256":"b7e18f4e23bb7218e1eb7697360c0209a60f4e58299c08f7acdd44d59a0137a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:09.021388Z","signature_b64":"2e2I9VotFM2lrLG1kawafNk/n/LWODvmAUQvg2uWOs5OdwVzkM810CtMQnl5a7E9QZUiCqekPdKlgtBAwTi5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94fc9307966ca94fbca5f414ac47a6388747233e251fdf6fe7c143113890abdd","last_reissued_at":"2026-05-18T01:36:09.020938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:09.020938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Applications of Uniform Sampling: Densest Subgraph and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Hossein Esfandiari, MohammadTaghi Hajiaghayi","submitted_at":"2015-06-15T08:08:55Z","abstract_excerpt":"Recently [Bhattacharya et al., STOC 2015] provide the first non-trivial algorithm for the densest subgraph problem in the streaming model with additions and deletions to its edges, i.e., for dynamic graph streams. They present a $(0.5-\\epsilon)$-approximation algorithm using $\\tilde{O}(n)$ space, where factors of $\\epsilon$ and $\\log(n)$ are suppressed in the $\\tilde{O}$ notation. However, the update time of this algorithm is large. To remedy this, they also provide a $(0.25-\\epsilon)$-approximation algorithm using $\\tilde{O}(n)$ space with update time $\\tilde{O}(1)$.\n  In this paper we improv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04505","kind":"arxiv","version":3},"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":"1506.04505","created_at":"2026-05-18T01:36:09.021015+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.04505v3","created_at":"2026-05-18T01:36:09.021015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04505","created_at":"2026-05-18T01:36:09.021015+00:00"},{"alias_kind":"pith_short_12","alias_value":"ST6JGB4WNSUU","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"ST6JGB4WNSUU7PFF","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"ST6JGB4W","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.12600","citing_title":"Fast and Simple Densest Subgraph with Predictions","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC","json":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC.json","graph_json":"https://pith.science/api/pith-number/ST6JGB4WNSUU7PFF6QKKYR5GHC/graph.json","events_json":"https://pith.science/api/pith-number/ST6JGB4WNSUU7PFF6QKKYR5GHC/events.json","paper":"https://pith.science/paper/ST6JGB4W"},"agent_actions":{"view_html":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC","download_json":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC.json","view_paper":"https://pith.science/paper/ST6JGB4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.04505&json=true","fetch_graph":"https://pith.science/api/pith-number/ST6JGB4WNSUU7PFF6QKKYR5GHC/graph.json","fetch_events":"https://pith.science/api/pith-number/ST6JGB4WNSUU7PFF6QKKYR5GHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC/action/storage_attestation","attest_author":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC/action/author_attestation","sign_citation":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC/action/citation_signature","submit_replication":"https://pith.science/pith/ST6JGB4WNSUU7PFF6QKKYR5GHC/action/replication_record"}},"created_at":"2026-05-18T01:36:09.021015+00:00","updated_at":"2026-05-18T01:36:09.021015+00:00"}