{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ALLKKDL6MU3ASV3NCH3NR3U7CX","short_pith_number":"pith:ALLKKDL6","schema_version":"1.0","canonical_sha256":"02d6a50d7e653609576d11f6d8ee9f15c274603b6106bb531a3ac5a4a72d47f4","source":{"kind":"arxiv","id":"1705.05646","version":1},"attestation_state":"computed","paper":{"title":"Quadratic and Near-Quadratic Lower Bounds for the CONGEST Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Ami Paz, Keren Censor-Hillel, Seri Khoury","submitted_at":"2017-05-16T11:11:37Z","abstract_excerpt":"We present the first super-linear lower bounds for natural graph problems in the CONGEST model, answering a long-standing open question.\n  Specifically, we show that any exact computation of a minimum vertex cover or a maximum independent set requires $\\Omega(n^2/\\log^2{n})$ rounds in the worst case in the CONGEST model, as well as any algorithm for $\\chi$-coloring a graph, where $\\chi$ is the chromatic number of the graph. We further show that such strong lower bounds are not limited to NP-hard problems, by showing two simple graph problems in P which require a quadratic and near-quadratic nu"},"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":"1705.05646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-16T11:11:37Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"3ecf0ae6ce05fa1f81c6c725b4f4e143df582f5ba439f09ca8318ec0676d355f","abstract_canon_sha256":"604e4a0bfa3ab20e371eb76d1dc0b85bb0611d58f3fe21bc33f2f2bd4b315838"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:20.572412Z","signature_b64":"4OurW33Kma6/smmCUHdUgakWQL4h9fJ3DjyrK/nuTX5CzZlWrF4BdC143hDnJ9JbHThjSM6o+rxnGOVAJ9WcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02d6a50d7e653609576d11f6d8ee9f15c274603b6106bb531a3ac5a4a72d47f4","last_reissued_at":"2026-05-18T00:44:20.571963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:20.571963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic and Near-Quadratic Lower Bounds for the CONGEST Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Ami Paz, Keren Censor-Hillel, Seri Khoury","submitted_at":"2017-05-16T11:11:37Z","abstract_excerpt":"We present the first super-linear lower bounds for natural graph problems in the CONGEST model, answering a long-standing open question.\n  Specifically, we show that any exact computation of a minimum vertex cover or a maximum independent set requires $\\Omega(n^2/\\log^2{n})$ rounds in the worst case in the CONGEST model, as well as any algorithm for $\\chi$-coloring a graph, where $\\chi$ is the chromatic number of the graph. We further show that such strong lower bounds are not limited to NP-hard problems, by showing two simple graph problems in P which require a quadratic and near-quadratic nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05646","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":"1705.05646","created_at":"2026-05-18T00:44:20.572033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.05646v1","created_at":"2026-05-18T00:44:20.572033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05646","created_at":"2026-05-18T00:44:20.572033+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALLKKDL6MU3A","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALLKKDL6MU3ASV3N","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALLKKDL6","created_at":"2026-05-18T12:31:05.417338+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/ALLKKDL6MU3ASV3NCH3NR3U7CX","json":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX.json","graph_json":"https://pith.science/api/pith-number/ALLKKDL6MU3ASV3NCH3NR3U7CX/graph.json","events_json":"https://pith.science/api/pith-number/ALLKKDL6MU3ASV3NCH3NR3U7CX/events.json","paper":"https://pith.science/paper/ALLKKDL6"},"agent_actions":{"view_html":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX","download_json":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX.json","view_paper":"https://pith.science/paper/ALLKKDL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.05646&json=true","fetch_graph":"https://pith.science/api/pith-number/ALLKKDL6MU3ASV3NCH3NR3U7CX/graph.json","fetch_events":"https://pith.science/api/pith-number/ALLKKDL6MU3ASV3NCH3NR3U7CX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX/action/storage_attestation","attest_author":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX/action/author_attestation","sign_citation":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX/action/citation_signature","submit_replication":"https://pith.science/pith/ALLKKDL6MU3ASV3NCH3NR3U7CX/action/replication_record"}},"created_at":"2026-05-18T00:44:20.572033+00:00","updated_at":"2026-05-18T00:44:20.572033+00:00"}