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

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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 $d$.


$n$: 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

D-Neighborhood of a String - Time.png