Frequent Words with Mismatches Problem: Difference between revisions
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[[File:Frequent Words with Mismatches Problem - Space.png|1000px]] | [[File:Frequent Words with Mismatches Problem - Space.png|1000px]] | ||
== | == Time-Space Tradeoff == | ||
[[File:Frequent Words with Mismatches Problem - Pareto Frontier.png|1000px]] | [[File:Frequent Words with Mismatches Problem - Pareto Frontier.png|1000px]] | ||
Revision as of 14:48, 15 February 2023
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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