The Frequent Words Problem: Difference between revisions
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== Parameters == | == Parameters == | ||
n: length of string | $n$: length of string | ||
k: length of words | $k$: length of words | ||
sigma: size of alphabet | $\sigma$: size of alphabet | ||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 20: | Line 20: | ||
|- | |- | ||
| [[Naive solution (The Frequent Words Problem The Frequent Words Problem)|Naive solution]] || 1940 || $O(n)$ || $O(max(n, sigma^k)$) | | [[Naive solution (The Frequent Words Problem The Frequent Words Problem)|Naive solution]] || 1940 || $O(n)$ || $O(max(n, \sigma^k)$) || Exact || Deterministic || | ||
|- | |- | ||
| [[Rabin Karp (The Frequent Words Problem The Frequent Words Problem)|Rabin Karp]] || 1987 || $O(n)$ || $O(max(n, sigma^k)$) | | [[Rabin Karp (The Frequent Words Problem The Frequent Words Problem)|Rabin Karp]] || 1987 || $O(n)$ || $O(max(n, \sigma^k)$)? || Exact || Deterministic || | ||
|- | |- | ||
|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:The Frequent Words Problem - Time.png|1000px]] | [[File:The Frequent Words Problem - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
http://bioinformaticsalgorithms.com/data/debugdatasets/replication/FrequentWordsProblem.pdf | http://bioinformaticsalgorithms.com/data/debugdatasets/replication/FrequentWordsProblem.pdf | ||
Latest revision as of 10:12, 28 April 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 | $O(n)$ | $O(max(n, \sigma^k)$) | Exact | Deterministic | |
| Rabin Karp | 1987 | $O(n)$ | $O(max(n, \sigma^k)$)? | Exact | Deterministic |
Time Complexity Graph
References/Citation
http://bioinformaticsalgorithms.com/data/debugdatasets/replication/FrequentWordsProblem.pdf