d-Neighborhood of a String (d-Neighborhood of a String)

Description

Given a DNA string pattern and an integer $d$, find the collection of strings that are within a $d$-neighborhood of the given pattern. A $d$-neighborhood is the set of all $k$-mers whose Hamming distance from the pattern is at most $d$.

Parameters

$n$: length of string

$d$: neighborhood distance threshold

$\sigma$: size of alphabet

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Iterative naive	1940	$O(f_{bin}(sigma-{1}, n, d)$) where f_{bin}(x, y, z) = sum_{i=0}^z C(y, i)*x^i	$O(n)$	Exact	Deterministic	Time

Time Complexity Graph