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

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Space Complexity Graph

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Time-Space Tradeoff

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