Frequent Words with Mismatches Problem: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Frequent Words with Mismatches Problem (Frequent Words with Mismatches Problem)}} == Description == Given two strings, determine the most frequent substring with at most $k$ mismatches, where mismatches are not counted towards the length of the substring. == Parameters == <pre>n: length of string k: length of words d: number of allowed mismatches sigma: size of alphabet</pre> == Table of Algorithms == {| class="wikitable sortable" style="text-alig...") |
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== Parameters == | == Parameters == | ||
$n$: length of string | |||
k: length of words | |||
d: number of allowed mismatches | $k$: length of words | ||
sigma: size of alphabet | |||
$d$: number of allowed mismatches | |||
$\sigma$: size of alphabet | |||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 23: | Line 26: | ||
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Frequent Words with Mismatches Problem - Time.png|1000px]] | [[File:Frequent Words with Mismatches Problem - Time.png|1000px]] | ||
Latest revision as of 09:12, 28 April 2023
Description
Given two strings, determine the most frequent substring with at most $k$ mismatches, where mismatches are not counted towards the length of the substring.
Parameters
$n$: length of string
$k$: length of words
$d$: number of allowed mismatches
$\sigma$: size of alphabet
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naive solution | 1940 | $O(n*f_{bin}(sigma-{1}, k, d)$) where f_{bin}(x, y, z) = sum_{i=0}^z C(y, i)*x^i | $O(max(n*f_{bin}(sigma-{1}, k, d)$, sigma^k)) auxiliary where f_{bin}(x, y, z) = sum_{i=0}^z C(y, i)*x^i | Exact | Deterministic |
Time Complexity Graph
