Cardinality Estimation: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Cardinality Estimation - Time.png|1000px]] | [[File:Cardinality Estimation - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Cardinality Estimation - Space.png|1000px]] | [[File:Cardinality Estimation - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Cardinality Estimation - Pareto Frontier.png|1000px]] | [[File:Cardinality Estimation - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
Given a multiset of (possibly hashed) values, estimate the number of distinct elements of the multiset. Of interest is minimizing storage usage.
Parameters
N: number of values in multiset
n: cardinality of multiset (not known)
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naive solution | 1940 | $O(N)$ | $O(n)$ | Exact | Deterministic | |
| Flajolet–Martin algorithm | 1984 | $O(N)$ | $O(log n)$ | Randomized | Time & Space | |
| LogLog algorithm | 2003 | $O(N)$ | $O(log(log(n)$)) | Randomized | Time & Space | |
| HyperLogLog algorithm | 2007 | $O(N)$ | $O(eps^{-2}*log(log(n)$))+log(n)) | Randomized | Time & Space | |
| HyperLogLog++ | 2014 | $O(N)$ | $O(eps^{-2}*log(log(n)$))+log(n)) | Randomized | Time |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
