{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:U2HNSAAVPTGSHRTNVMG4VFMKUR","short_pith_number":"pith:U2HNSAAV","schema_version":"1.0","canonical_sha256":"a68ed900157ccd23c66dab0dca958aa479a4f3911c3de6df537bb1ba3ee96eec","source":{"kind":"arxiv","id":"2412.12589","version":2},"attestation_state":"computed","paper":{"title":"Round and Communication Efficient Graph Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Farrel D Salim, Gopinath Mishra, Hung Thuan Nguyen, Yi-Jun Chang","submitted_at":"2024-12-17T06:46:09Z","abstract_excerpt":"In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\\Delta$. We consider a scenario where the edges of $G$ are partitioned between two players.\n  Our first contribution is a randomized protocol that efficiently finds a $(\\Delta + 1)$-vertex coloring of $G$, utilizing $O(n)$ bits of communication in expectation and completing in $O(\\log \\log n \\cdot \\log \\Delta)$ rounds in the worst case. This advancement represents a significant improvement over the work of Flin an"},"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":"2412.12589","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-12-17T06:46:09Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"a881e323ce4721e4585060e30da17f917e0d6ba64b0c4b1c363b2fdf8a415133","abstract_canon_sha256":"2f97dfd8ef7a7426ea53c8c6fa75db141f785f5de9858f9e99b12340f8363d28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:00:41.039061Z","signature_b64":"zL0ItT+pn7Wv6YHtO1qy6r6ELWtiJZdDkL2F6gPJox+JfFBZA5AbPkxLyPMBdGlgg4Hfekwcyy1Jg2qy4vskCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68ed900157ccd23c66dab0dca958aa479a4f3911c3de6df537bb1ba3ee96eec","last_reissued_at":"2026-07-05T11:00:41.038571Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:00:41.038571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Round and Communication Efficient Graph Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Farrel D Salim, Gopinath Mishra, Hung Thuan Nguyen, Yi-Jun Chang","submitted_at":"2024-12-17T06:46:09Z","abstract_excerpt":"In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\\Delta$. We consider a scenario where the edges of $G$ are partitioned between two players.\n  Our first contribution is a randomized protocol that efficiently finds a $(\\Delta + 1)$-vertex coloring of $G$, utilizing $O(n)$ bits of communication in expectation and completing in $O(\\log \\log n \\cdot \\log \\Delta)$ rounds in the worst case. This advancement represents a significant improvement over the work of Flin an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12589","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.12589/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.12589","created_at":"2026-07-05T11:00:41.038625+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.12589v2","created_at":"2026-07-05T11:00:41.038625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.12589","created_at":"2026-07-05T11:00:41.038625+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2HNSAAVPTGS","created_at":"2026-07-05T11:00:41.038625+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2HNSAAVPTGSHRTN","created_at":"2026-07-05T11:00:41.038625+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2HNSAAV","created_at":"2026-07-05T11:00:41.038625+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.19729","citing_title":"Faster Dynamic $(\\Delta+1)$-Coloring Against Adaptive Adversaries","ref_index":2020,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR","json":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR.json","graph_json":"https://pith.science/api/pith-number/U2HNSAAVPTGSHRTNVMG4VFMKUR/graph.json","events_json":"https://pith.science/api/pith-number/U2HNSAAVPTGSHRTNVMG4VFMKUR/events.json","paper":"https://pith.science/paper/U2HNSAAV"},"agent_actions":{"view_html":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR","download_json":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR.json","view_paper":"https://pith.science/paper/U2HNSAAV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.12589&json=true","fetch_graph":"https://pith.science/api/pith-number/U2HNSAAVPTGSHRTNVMG4VFMKUR/graph.json","fetch_events":"https://pith.science/api/pith-number/U2HNSAAVPTGSHRTNVMG4VFMKUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR/action/storage_attestation","attest_author":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR/action/author_attestation","sign_citation":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR/action/citation_signature","submit_replication":"https://pith.science/pith/U2HNSAAVPTGSHRTNVMG4VFMKUR/action/replication_record"}},"created_at":"2026-07-05T11:00:41.038625+00:00","updated_at":"2026-07-05T11:00:41.038625+00:00"}