{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2EGGFF4VBPAKHCTY4LH5GMNVNC","short_pith_number":"pith:2EGGFF4V","schema_version":"1.0","canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","source":{"kind":"arxiv","id":"1503.03155","version":3},"attestation_state":"computed","paper":{"title":"Computing Heat Kernel Pagerank and a Local Clustering Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fan Chung, Olivia Simpson","submitted_at":"2015-03-11T02:47:50Z","abstract_excerpt":"Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time $O\\big(\\frac{\\log(\\epsilon^{-1})\\log n}{\\epsilon^3\\log\\log(\\epsilon^{-1})}\\big)$, assuming performing a random walk step and sampling from a distribution with bounded support take constant time.\n  The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms."},"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":"1503.03155","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-11T02:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"b7a848ccd672dafabfe2f2c1b0c97ca3f8dab4025e2a5da13daec241b223e678","abstract_canon_sha256":"fdbc0dfa83ef5acf834a6ca89d028736522dc29a4d4ed285b8b63dabfb440f65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.278212Z","signature_b64":"cLBChoy5o1WI9c+/DvY+JReqFVLhnVpfKhersToF5Q6bx7C5dpd3eTqBke7aY6584X7UD4BPk74ubDPcaZhpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10c6297950bc0a38a78e2cfd331b568a8f0b5a52da96b7ebc45ca6d7e8485e4","last_reissued_at":"2026-05-18T00:54:58.277665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.277665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Heat Kernel Pagerank and a Local Clustering Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fan Chung, Olivia Simpson","submitted_at":"2015-03-11T02:47:50Z","abstract_excerpt":"Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time $O\\big(\\frac{\\log(\\epsilon^{-1})\\log n}{\\epsilon^3\\log\\log(\\epsilon^{-1})}\\big)$, assuming performing a random walk step and sampling from a distribution with bounded support take constant time.\n  The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03155","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":"1503.03155","created_at":"2026-05-18T00:54:58.277748+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03155v3","created_at":"2026-05-18T00:54:58.277748+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03155","created_at":"2026-05-18T00:54:58.277748+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EGGFF4VBPAK","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EGGFF4VBPAKHCTY","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EGGFF4V","created_at":"2026-05-18T12:28:59.999130+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/2EGGFF4VBPAKHCTY4LH5GMNVNC","json":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC.json","graph_json":"https://pith.science/api/pith-number/2EGGFF4VBPAKHCTY4LH5GMNVNC/graph.json","events_json":"https://pith.science/api/pith-number/2EGGFF4VBPAKHCTY4LH5GMNVNC/events.json","paper":"https://pith.science/paper/2EGGFF4V"},"agent_actions":{"view_html":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC","download_json":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC.json","view_paper":"https://pith.science/paper/2EGGFF4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03155&json=true","fetch_graph":"https://pith.science/api/pith-number/2EGGFF4VBPAKHCTY4LH5GMNVNC/graph.json","fetch_events":"https://pith.science/api/pith-number/2EGGFF4VBPAKHCTY4LH5GMNVNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/action/storage_attestation","attest_author":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/action/author_attestation","sign_citation":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/action/citation_signature","submit_replication":"https://pith.science/pith/2EGGFF4VBPAKHCTY4LH5GMNVNC/action/replication_record"}},"created_at":"2026-05-18T00:54:58.277748+00:00","updated_at":"2026-05-18T00:54:58.277748+00:00"}