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

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

Space Complexity graph

Pareto Decades graph