d-Neighborhood of a String

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

Parameters

  • nn: length of string
  • dd: neighborhood distance threshold
  • σ\sigma: size of alphabet

Filters

Computational Model

Randomization

Approximation

Algorithms Table

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Iterative naive1940O(fbin(σ1,n,d))O(f_{bin}(\sigma-1, n, d)) where fbin(x,y,z)=i=0z(yi)xif_{bin}(x, y, z) = \sum_{i=0}^z \binom{y}{i}x^iO(n)O(n)

Reductions Table

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Other relevant algorithms

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