{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JO662S362EVDUGDAR5DLM5LNJP","short_pith_number":"pith:JO662S36","schema_version":"1.0","canonical_sha256":"4bbded4b7ed12a3a18608f46b6756d4bf04e5aa67c94b8122c38064800e04a43","source":{"kind":"arxiv","id":"1102.2906","version":2},"attestation_state":"computed","paper":{"title":"A Tight Lower Bound on Distributed Random Walk Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan","submitted_at":"2011-02-14T21:32:54Z","abstract_excerpt":"We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show that a random walk of length $\\ell$ on a network of diameter $D$ can be performed in $\\tilde O(\\sqrt{\\ell D}+D)$ time. A major question left open is whether there exists a faster algorithm, especially whether the multiplication of $\\sqrt{\\ell}$ and $\\sqrt{D}$ is necessary.\n  In this paper, we show a tight unconditional lower bound on the time complexity of d"},"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":"1102.2906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2011-02-14T21:32:54Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8f3a4d5cc6ac737c0b194fd446640c8475bee0b3dadcb157573317653814aeb2","abstract_canon_sha256":"4daa73331adee8595166d23f3cb43e389f820a3ced431d5b533f953a29ebabc5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:56.891291Z","signature_b64":"uA01jWzghBOb5GV38aBlLpmgI88KabIQKy4s5TrSguYKLjH0DYcqPqu6sBwszm6lPFT0eZTee5e+fKo0M7EbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bbded4b7ed12a3a18608f46b6756d4bf04e5aa67c94b8122c38064800e04a43","last_reissued_at":"2026-05-18T04:10:56.890678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:56.890678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Tight Lower Bound on Distributed Random Walk Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan","submitted_at":"2011-02-14T21:32:54Z","abstract_excerpt":"We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show that a random walk of length $\\ell$ on a network of diameter $D$ can be performed in $\\tilde O(\\sqrt{\\ell D}+D)$ time. A major question left open is whether there exists a faster algorithm, especially whether the multiplication of $\\sqrt{\\ell}$ and $\\sqrt{D}$ is necessary.\n  In this paper, we show a tight unconditional lower bound on the time complexity of d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2906","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":""},"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":"1102.2906","created_at":"2026-05-18T04:10:56.890751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.2906v2","created_at":"2026-05-18T04:10:56.890751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2906","created_at":"2026-05-18T04:10:56.890751+00:00"},{"alias_kind":"pith_short_12","alias_value":"JO662S362EVD","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JO662S362EVDUGDA","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JO662S36","created_at":"2026-05-18T12:26:32.869790+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/JO662S362EVDUGDAR5DLM5LNJP","json":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP.json","graph_json":"https://pith.science/api/pith-number/JO662S362EVDUGDAR5DLM5LNJP/graph.json","events_json":"https://pith.science/api/pith-number/JO662S362EVDUGDAR5DLM5LNJP/events.json","paper":"https://pith.science/paper/JO662S36"},"agent_actions":{"view_html":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP","download_json":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP.json","view_paper":"https://pith.science/paper/JO662S36","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.2906&json=true","fetch_graph":"https://pith.science/api/pith-number/JO662S362EVDUGDAR5DLM5LNJP/graph.json","fetch_events":"https://pith.science/api/pith-number/JO662S362EVDUGDAR5DLM5LNJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP/action/storage_attestation","attest_author":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP/action/author_attestation","sign_citation":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP/action/citation_signature","submit_replication":"https://pith.science/pith/JO662S362EVDUGDAR5DLM5LNJP/action/replication_record"}},"created_at":"2026-05-18T04:10:56.890751+00:00","updated_at":"2026-05-18T04:10:56.890751+00:00"}