Table 1 Comparative characteristics of Bloom filters and Cuckoo filters (Notation: m≡number of buckets for Cuckoo or size of the array for Bloom; n≡number of items; b≡bucket size for Cuckoo; α≡load factor 0 ≤ α ≤ 1; k≡number of hash functions; f≡fingerprint length in bits for Cuckoo; n/a≡not applicable)

Lookup operation

O(k)

O(1)

maximum of two buckets to check

Insert operation

O(k)

O(1)

longer as load factor approaches capacity

Delete operation

N/a

O(1)

maximum of two buckets to inspect

Number of hash functions k_opt

\(\left( {\frac{m}{n}} \right) \cdot {\text{ln 2}}\)

to minimize false positive rate

2

to achieve the close-to-best space efficiency for the most common acceptable false positive rate

Minimal fingerprint size (bits)

N/a

\(\left\lceil {\log _{2} \left( {\frac{1}{{\varepsilon _{{Cuckoo\;filter}} }}} \right) + \log _{2} \left( {2b} \right)} \right\rceil\)

Best number of entries per bucket b

N/a

4

to achieve the close-to-best space efficiency for the most common acceptable false positive rate

Bits per item (load factor = 95.5%)

\(1.44\log _{2} \left( {\frac{1}{{\varepsilon _{{Bloom\,filter}} }}} \right)\)

\(1.05\left( {\log _{2} \left( {\frac{1}{{\varepsilon _{{Cuckoo\;filter}} }}} \right) + \log _{2} \left( {2b} \right)} \right)\)