{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BCAOOVTN7QHSZH33XIM7FGIBDZ","short_pith_number":"pith:BCAOOVTN","schema_version":"1.0","canonical_sha256":"0880e7566dfc0f2c9f7bba19f299011e46c6c08b3be212a3f2fab7643ccc6144","source":{"kind":"arxiv","id":"1804.09684","version":1},"attestation_state":"computed","paper":{"title":"Power of $d$ Choices with Simple Tabulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anders Aamand, Mathias B{\\ae}k Tejs Knudsen, Mikkel Thorup","submitted_at":"2018-04-25T17:23:48Z","abstract_excerpt":"Suppose that we are to place $m$ balls into $n$ bins sequentially using the $d$-choice paradigm: For each ball we are given a choice of $d$ bins, according to $d$ hash functions $h_1,\\dots,h_d$ and we place the ball in the least loaded of these bins breaking ties arbitrarily. Our interest is in the number of balls in the fullest bin after all $m$ balls have been placed.\n  Azar et al. [STOC'94] proved that when $m=O(n)$ and when the hash functions are fully random the maximum load is at most $\\frac{\\lg \\lg n }{\\lg d}+O(1)$ whp (i.e. with probability $1-O(n^{-\\gamma})$ for any choice of $\\gamma$"},"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":"1804.09684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-25T17:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"951e4fce2092958226ec3d6c1e1e20356acb23a8cafd4434654b8c59fd68b83b","abstract_canon_sha256":"4f3ba4e0e8441afd8a425d2a2af76d40712fe2cb6caeee04f3900643659b660f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:31.078169Z","signature_b64":"v5jbPR5c8wFwbJt71CWiHrLqDljUV6TfNESathrXB8GCQ/VZUR7oY0AIEhTxSBPp8axd+AxSgTM16Ah7p9ZIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0880e7566dfc0f2c9f7bba19f299011e46c6c08b3be212a3f2fab7643ccc6144","last_reissued_at":"2026-05-18T00:17:31.077456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:31.077456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power of $d$ Choices with Simple Tabulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anders Aamand, Mathias B{\\ae}k Tejs Knudsen, Mikkel Thorup","submitted_at":"2018-04-25T17:23:48Z","abstract_excerpt":"Suppose that we are to place $m$ balls into $n$ bins sequentially using the $d$-choice paradigm: For each ball we are given a choice of $d$ bins, according to $d$ hash functions $h_1,\\dots,h_d$ and we place the ball in the least loaded of these bins breaking ties arbitrarily. Our interest is in the number of balls in the fullest bin after all $m$ balls have been placed.\n  Azar et al. [STOC'94] proved that when $m=O(n)$ and when the hash functions are fully random the maximum load is at most $\\frac{\\lg \\lg n }{\\lg d}+O(1)$ whp (i.e. with probability $1-O(n^{-\\gamma})$ for any choice of $\\gamma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09684","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":"1804.09684","created_at":"2026-05-18T00:17:31.077575+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09684v1","created_at":"2026-05-18T00:17:31.077575+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09684","created_at":"2026-05-18T00:17:31.077575+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCAOOVTN7QHS","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCAOOVTN7QHSZH33","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCAOOVTN","created_at":"2026-05-18T12:32:13.499390+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/BCAOOVTN7QHSZH33XIM7FGIBDZ","json":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ.json","graph_json":"https://pith.science/api/pith-number/BCAOOVTN7QHSZH33XIM7FGIBDZ/graph.json","events_json":"https://pith.science/api/pith-number/BCAOOVTN7QHSZH33XIM7FGIBDZ/events.json","paper":"https://pith.science/paper/BCAOOVTN"},"agent_actions":{"view_html":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ","download_json":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ.json","view_paper":"https://pith.science/paper/BCAOOVTN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09684&json=true","fetch_graph":"https://pith.science/api/pith-number/BCAOOVTN7QHSZH33XIM7FGIBDZ/graph.json","fetch_events":"https://pith.science/api/pith-number/BCAOOVTN7QHSZH33XIM7FGIBDZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ/action/storage_attestation","attest_author":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ/action/author_attestation","sign_citation":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ/action/citation_signature","submit_replication":"https://pith.science/pith/BCAOOVTN7QHSZH33XIM7FGIBDZ/action/replication_record"}},"created_at":"2026-05-18T00:17:31.077575+00:00","updated_at":"2026-05-18T00:17:31.077575+00:00"}