# The Bloomier filter: an efficient data structure for static support lookup tables

@inproceedings{Chazelle2004TheBF, title={The Bloomier filter: an efficient data structure for static support lookup tables}, author={Bernard Chazelle and Joe Kilian and Ronitt Rubinfeld and Ayellet Tal}, booktitle={SODA '04}, year={2004} }

We introduce the Bloomier filter, a data structure for compactly encoding a function with static support in order to support approximate evaluation queries. Our construction generalizes the classical Bloom filter, an ingenious hashing scheme heavily used in networks and databases, whose main attribute---space efficiency---is achieved at the expense of a tiny false-positive rate. Whereas Bloom filters can handle only set membership queries, our Bloomier filters can deal with arbitrary functions…

## 403 Citations

A Shifting Bloom Filter Framework for Set Queries

- Computer ScienceProc. VLDB Endow.
- 2016

This paper proposes a Shifting Bloom Filter framework for representing and querying sets, and demonstrates the effectiveness of ShBF using three types of popular set queries: membership, association, and multiplicity queries.

Bloomier Filters: A second look

- Computer ScienceESA
- 2008

This article gives a simple construction of a Bloomier filter, a space efficient structure for storing static sets, where the space efficiency is gained at the expense of a small probability of false-positives.

Counting with TinyTable: Every bit counts!

- Computer Science2015 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)
- 2015

TinyTable is presented, an efficient hash table based construction that supports membership queries, multiplicity queries (statistics) and removals, and is more space efficient than existing alternatives, both those derived from Bloom filters and other hashtable based schemes.

Counting With Tinytable: Every Bit Counts!

- Computer ScienceIEEE Access
- 2019

TinyTable is presented that supports set membership, removals, and multiplicity queries, and is more compact than Bloom filters as long as the false positive ratio is less than 1%.

Incremental Bloom Filters

- Computer ScienceIEEE INFOCOM 2008 - The 27th Conference on Computer Communications
- 2008

This work considers the problem of minimizing the memory requirements in cases where the number of elements in the set is not known in advance but the distribution or moment information of the numberof elements is known and shows how to exploit such information to minimize the expected amount of memory required for the filter.

Optimizing data popularity conscious bloom filters

- Computer SciencePODC '08
- 2008

This paper studies the problem of minimizing the false-positive probability of a Bloom filter by adapting the number of hashes used for each data object to its popularity in sets and membership queries and proposes two polynomial-time solutions with bounded approximation ratios.

Rank-indexed hashing: A compact construction of Bloom filters and variants

- Computer Science2008 IEEE International Conference on Network Protocols
- 2008

A new fingerprint hash table construction called Rank-Indexed Hashing that can achieve very compact representations is proposed that can be achieved with a factor of three or more in space savings even for a false positive probability of just 1%.

Fast Bloom Filters and Their Generalization

- Computer ScienceIEEE Transactions on Parallel and Distributed Systems
- 2014

Bloom-1, a data structure that performs membership check in one memory access, which compares favorably with the k memory accesses of a standard Bloom filter, is studied, allowing performance tradeoff between membership query overhead and false positive ratio.

Bloom Maps

- Computer ScienceANALCO
- 2008

A novel data structure, the Bloom map, is introduced, generalising the Bloom filter to this problem of succinctly encoding a static map to support approximate queries and derives upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys.

Achieving Perfect Hashing through an Improved Construction of Bloom Filters

- Computer Science2010 IEEE International Conference on Communications
- 2010

This paper proposes a scheme to extend BFs with ``indexing'' features so that when an element is queried, an univocal index of that element is returned, which in turn can be used as an address for a table, just as a perfect hashing scheme.

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