The Frequent Words Problem: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:The Frequent Words Problem - Time.png|1000px]] | [[File:The Frequent Words Problem - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:The Frequent Words Problem - Space.png|1000px]] | [[File:The Frequent Words Problem - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:The Frequent Words Problem - Pareto Frontier.png|1000px]] | [[File:The Frequent Words Problem - Pareto Frontier.png|1000px]] | ||
Revision as of 13:05, 15 February 2023
Description
Given a string of length $n$ and in input integer $k$, determine the most frequent $k$-mers in the string, i.e. the most frequent words of length $k$.
Parameters
n: length of string
k: length of words
sigma: size of alphabet
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naive solution | 1940 | $O(n)$ | $O(max(n, sigma^k)$) auxiliary | Exact | Deterministic | |
| Rabin Karp | 1987 | $O(n)$ | $O(max(n, sigma^k)$) auxiliary? | Exact | Deterministic |
Time Complexity Graph
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Space Complexity Graph
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Pareto Frontier Improvements Graph
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References/Citation
http://bioinformaticsalgorithms.com/data/debugdatasets/replication/FrequentWordsProblem.pdf