{
  "slug": "scalable-bloom-filter",
  "term": "Scalable Bloom filter",
  "aliases": [],
  "definition": "A scalable Bloom filter grows a chain of membership filters with progressively tighter false-positive budgets as the represented set expands.",
  "note": "Growth: New sub-filters are added as existing ones reach their occupancy limit. A lookup is positive if any sub-filter answers positive. Older filters remain represented; this is growth, not an aging policy that forgets old keys. [scalable-paper]\n\nError budget: For a target P and tightening ratio 0 < r < 1, assign sub-filter i the bound P(1-r)r^i, starting at i=0. If those bounds hold for the absent-key query population, the union bound limits the whole chain to P without requiring independent sub-filter errors. Multiplying negative probabilities needs an independence assumption. [scalable-paper]\n\nExample: For P=1% and r=0.5, the first three budgets are 0.5%, 0.25% and 0.125%. Their sum is 0.875%, leaving 0.125% for all later filters. These are allocated bounds, not measured error rates.\n\nResource trade-off: More sub-filters consume memory and query work. Larger capacity expansion reduces their number but reserves more space before it is needed. Capacity expansion and error tightening are separate parameters. [scalable-paper] Documented non-scaling mode rejects additions when capacity is exhausted instead of extending the chain. [reserve]",
  "status": "shipping",
  "advantages": [],
  "limitations": [
    {
      "text": "The error budget does not provide a fixed memory ceiling, deletion support or a bound against adaptively chosen queries.",
      "citationIds": [
        "scalable-paper",
        "adaptive-amq"
      ]
    }
  ],
  "related": [
    "bloom-filter",
    "stable-bloom-filter",
    "counting-bloom-filter",
    "lsm-tree"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-11-10",
  "citations": [
    {
      "id": "scalable-paper",
      "title": "Almeida, Baquero, Preguica and Hutchison. Scalable Bloom Filters. IPL 101(6), 2007, pp. 255-261, section 4. DOI: 10.1016/j.ipl.2006.10.007.",
      "url": "https://asc.di.fct.unl.pt/~nmp/pubs/ipl-2007.pdf",
      "accessed": "2026-11-10"
    },
    {
      "id": "reserve",
      "title": "Redis documentation. BF.RESERVE: capacity, expansion, NONSCALING and sub-filter overhead.",
      "url": "https://redis.io/docs/latest/commands/bf.reserve/",
      "accessed": "2026-11-10"
    },
    {
      "id": "adaptive-amq",
      "title": "Bender et al. Bloom Filters, Adaptivity, and the Dictionary Problem. arXiv:1711.01616v3 (2018), sections 1-4.",
      "url": "https://arxiv.org/abs/1711.01616v3",
      "accessed": "2026-11-10"
    }
  ],
  "provenance": [
    "Shipping status reflects documented auto-scaling Bloom-filter support in Redis. The illustrative P and r budget does not specify that implementation's parameter mapping. [reserve]",
    "The original paper analyzes partitioned sub-filters and space/growth trade-offs; its plots are not a contemporary storage-engine latency benchmark. [scalable-paper]",
    "The 1% example is geometric-series arithmetic. The chain bound assumes valid per-filter error bounds for the same query population, not adversarial robustness. [adaptive-amq]"
  ]
}