Single String Search: Difference between revisions
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| [[Naïve string-search algorithm (Single String Search String Search)|Naïve string-search algorithm]] || 1940 || $O(m(n-m+{1}))$ || $O({1})$ || Exact || Deterministic || | | [[Naïve string-search algorithm (Single String Search String Search)|Naïve string-search algorithm]] || 1940 || $O(m(n-m+{1}))$ || $O({1})$ || Exact || Deterministic || | ||
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| [[Knuth-Morris-Pratt (KMP) algorithm (Single String Search String Search)|Knuth-Morris-Pratt (KMP) algorithm]] || 1977 || $O(m+n)$ || $O(m)$ || Exact || Deterministic || [https://pdfs.semanticscholar.org/4479/9559a1067e06b5a6bf052f8f10637707928f.pdf Time | | [[Knuth-Morris-Pratt (KMP) algorithm (Single String Search String Search)|Knuth-Morris-Pratt (KMP) algorithm]] || 1977 || $O(m+n)$ || $O(m)$ || Exact || Deterministic || [https://pdfs.semanticscholar.org/4479/9559a1067e06b5a6bf052f8f10637707928f.pdf Time & Space] | ||
|- | |- | ||
| [[Boyer-Moore (BM) algorithm (Single String Search String Search)|Boyer-Moore (BM) algorithm]] || 1977 || $O(mn + s)$ || $O(s)$ || Exact || Deterministic || [https://www.cs.utexas.edu/users/moore/publications/fstrpos.pdf Time & Space] | | [[Boyer-Moore (BM) algorithm (Single String Search String Search)|Boyer-Moore (BM) algorithm]] || 1977 || $O(mn + s)$ || $O(s)$ || Exact || Deterministic || [https://www.cs.utexas.edu/users/moore/publications/fstrpos.pdf Time & Space] | ||
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[[File:String Search - Single String Search - Time.png|1000px]] | [[File:String Search - Single String Search - Time.png|1000px]] | ||
Latest revision as of 09:07, 28 April 2023
Description
Single string search algorithms try to find a place where a string (also called a pattern) is found within a larger string or text.
Related Problems
Related: Multiple String Search
Parameters
$m$: pattern length
$n$: length of searchable text
$s$: size of the alphabet
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naïve string-search algorithm | 1940 | $O(m(n-m+{1}))$ | $O({1})$ | Exact | Deterministic | |
| Knuth-Morris-Pratt (KMP) algorithm | 1977 | $O(m+n)$ | $O(m)$ | Exact | Deterministic | Time & Space |
| Boyer-Moore (BM) algorithm | 1977 | $O(mn + s)$ | $O(s)$ | Exact | Deterministic | Time & Space |
| Rabin-Karp (RK) algorithm | 1987 | $O(mn)$ | $O({1})$ | Exact | Deterministic | Time |
| Bitap algorithm | 1964 | $O(mn)$ | $O(m)$ | Exact | Deterministic | Time |
| Tuned Boyer-Moore algorithm | 1991 | $O(mn)$ | $O(m + s)$ | Exact | Deterministic | Time & Space |
| Two-way String-Matching Algorithm | 1991 | $O(n + m)$ | $O({1})$ | Exact | Deterministic | Time & Space |
| String-Matching with Finite Automata | 1940 | $O(mn)$ | $O(m)$ | Exact | Deterministic | |
| Quick-Skip Searching | 2012 | $O(mn)$ | $O(m)$ | Exact | Deterministic | Time |
| Fast Hybrid Algorithm | 2017 | $O(n+m)$+ $O(m+s)$ | $O(m)$ | Exact | Deterministic | Time |
| Backward Non-Deterministic DAWG Matching (BNDM) | 1998 | $O(n+m)$ | $O(sm)$ | Exact | Parallel | Time & Space |
| Boyer-Moore-Horspool (BMH) | 1980 | $O(mn + s)$ | $O(s)$ | Exact | Deterministic | Time |
| Raita Algorithm | 1991 | $O(mn + s)$ | $O(s)$ | Exact | Deterministic | Time |
| BOM (Backward Oracle Matching) | 1999 | $O(m)$ + $O(mn)$ | $O(m)$ | Exact | Deterministic | Time & Space |
| Apostolico–Giancarlo Algorithm | 1986 | $O(m + s)$ + $O(n)$ | $O(m)$ | Exact | Deterministic | Time & Space |
| 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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