{"paper":{"title":"DynamicLogLog: Faster, Smaller, and More Accurate Cardinality Estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"DynamicLogLog stores relative leading-zero counts with a shared exponent to cut memory by one-third while removing HyperLogLog's error spike and adding an early-exit mask.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Brian Bushnell","submitted_at":"2026-03-28T20:52:33Z","abstract_excerpt":"Cardinality estimation - calculating the number of distinct elements in a stream - is a longstanding problem with applications from networking to bioinformatics. HyperLogLog (HLL), the prevailing standard, has a well-known error spike in its transition region and requires 6 bits per bucket, with data structure size scaling as B*log(log(cardinality)). We present DynamicLogLog (DLL), which uses a shared exponent across all buckets, storing only relative leading-zero counts. This yields three benefits: (1) only 4 bits per bucket (33% memory reduction), (2) an early exit mask that rejects >99.9% o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"At 2,048 buckets with 512k simulations, DLL4's hybrid estimate achieves 1.830% mean and 1.834% peak absolute error using 1,024 bytes, compared to 1.84% mean and 34.1% peak for HLL using 1,536 bytes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the early-exit mask and hybrid blend maintain their reported accuracy and speed on real-world data distributions rather than only on the synthetic streams used in the 512k simulations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"DynamicLogLog cuts memory by 33%, speeds up queries over 10x in bandwidth-limited cases, and removes HyperLogLog's transition-region error spike while matching or beating accuracy.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"DynamicLogLog stores relative leading-zero counts with a shared exponent to cut memory by one-third while removing HyperLogLog's error spike and adding an early-exit mask.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0038df3c4a0ca1ac45be0659ce2bf3a15cb7e28fff02f917ac11cf59d186d085"},"source":{"id":"2603.27405","kind":"arxiv","version":2},"verdict":{"id":"33023362-5753-4f00-88d0-bfc2c726af05","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T21:16:30.098530Z","strongest_claim":"At 2,048 buckets with 512k simulations, DLL4's hybrid estimate achieves 1.830% mean and 1.834% peak absolute error using 1,024 bytes, compared to 1.84% mean and 34.1% peak for HLL using 1,536 bytes.","one_line_summary":"DynamicLogLog cuts memory by 33%, speeds up queries over 10x in bandwidth-limited cases, and removes HyperLogLog's transition-region error spike while matching or beating accuracy.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the early-exit mask and hybrid blend maintain their reported accuracy and speed on real-world data distributions rather than only on the synthetic streams used in the 512k simulations.","pith_extraction_headline":"DynamicLogLog stores relative leading-zero counts with a shared exponent to cut memory by one-third while removing HyperLogLog's error spike and adding an early-exit mask."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4f57b7bea4eddbe1300f4734a6c319fd9e6a6f25532cce7f361663bc9ebcbd06"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}