Frequent Words with Mismatches Problem: Difference between revisions

From Algorithm Wiki
Jump to navigation Jump to search
(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...")
 
No edit summary
Line 6: Line 6:
== Parameters ==  
== Parameters ==  


<pre>n: length of string
n: length of string
 
k: length of words
k: length of words
d: number of allowed mismatches
d: number of allowed mismatches
sigma: size of alphabet</pre>
 
sigma: size of alphabet


== Table of Algorithms ==  
== Table of Algorithms ==  

Revision as of 12:03, 15 February 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

Error creating thumbnail: Unable to save thumbnail to destination

Space Complexity graph

Error creating thumbnail: Unable to save thumbnail to destination

Pareto Decades graph

Error creating thumbnail: Unable to save thumbnail to destination