Multiple String Search (String Search)
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Description
Multiple string search algorithms try to find a place where one or several strings (also called patterns) are found within a larger string or text.
Related Problems
Related: Single String Search
Parameters
$m$: longest pattern length
$n$: length of searchable text
$s$: size of the alphabet
$k$: number of patterns to search for
$z$: number of matches
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Commentz-Walter Algorithm | 1979 | $O(mn)$ | $O(km)$ | Exact | Deterministic | Time |
| Aho–Corasick (AC) Algorithm | 1975 | $O(n + m + z)$ | $O(km)$ | Exact | Deterministic | Time |
| Wu and Manber, Fuzzy String Matching | 1992 | $O(nk \lceil m/w \rceil)$ | $O(ms + k \lceil m/w \rceil)$ | Levensthein Distance = k | Deterministic | Time & Space |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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