D-Neighborhood of a String: Difference between revisions
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(Created page with "{{DISPLAYTITLE: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 == <pre>n: length of string d: neighborhood distance threshold sigma: size of alphabet</pre> == Table of Algorithms == {| cla...") |
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== Parameters == | == Parameters == | ||
$n$: length of string | |||
d: neighborhood distance threshold | |||
sigma: size of alphabet | $d$: neighborhood distance threshold | ||
$\sigma$: size of alphabet | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Iterative naive (d-Neighborhood of a String d-Neighborhood of a String)|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 || $O(n)$ | | [[Iterative naive (d-Neighborhood of a String d-Neighborhood of a String)|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 || [http://rosalind.info/problems/ba1n/ Time] | ||
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== Time Complexity Graph == | |||
[[File:d-Neighborhood of a String - Time.png|1000px]] | |||
Latest revision as of 09:11, 28 April 2023
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
