Lesson plan
Two-way string-matching algorithm
In computer science, the two-way string-matching algorithm (or Crochemore-Perrin string-matching algorithm) is a string-searching algorithm, discovered by Maxime Crochemore and Dominique Perrin in 1991. It searches for copies of a "needle" of length m in a "haystack" of length n. After preprocessing the needle in time O(m), the actual search takes time O(n) linear in the length of the haystack. The two-way algorithm can be viewed as a combination of the forward-going Knuth–Morris–Pratt algorithm (KMP) and the backward-running Boyer–Moore string-search algorithm (BM). Like those two, the two-way algorithm preprocesses the needle to find partially repeating periods and computes “shifts” based on them, indicating what offset to “jump” to in the haystack when a given character is encountered. Unlike BM and KMP, it uses only O(1) additional space to store information about those partial repeats (assuming the transdichotomous model, where an index of ⌈log 2 (m)⌉ bits is counted as a single word). The preprocessing computes the "period" of the needle, the minimum offset between two consecutive matches (a value between 1 and m), and a "critical factorization" of the needle into a prefix and suffix with particular properties, specified by the length of the prefix (also less than m). The actual matching operation performs at most 2n − m comparisons.…
Article summary
In computer science, the two-way string-matching algorithm (or Crochemore-Perrin string-matching algorithm) is a string-searching algorithm, discovered by Maxime Crochemore and Dominique Perrin in 1991. It searches for copies of a "needle" of length m in a "haystack" of length n. After preprocessing the needle in time O(m), the actual search takes time O(n) linear in the length of the haystack. The two-way algorithm can be viewed as a combination of the forward-going Knuth–Morris–Pratt algorithm (KMP) and the backward-running Boyer–Moore string-search algorithm (BM). Like those two, the two-way algorithm preprocesses the needle to find partially repeating periods and computes “shifts” based on them, indicating what offset to “jump” to in the haystack when a given character is encountered. Unlike BM and KMP, it uses only O(1) additional space to store information about those partial repeats (assuming the transdichotomous model, where an index of ⌈log 2 (m)⌉ bits is counted as a single word). The preprocessing computes the "period" of the needle, the minimum offset between two consecutive matches (a value between 1 and m), and a "critical factorization" of the needle into a prefix and suffix with particular properties, specified by the length of the prefix (also less than m). The actual matching operation performs at most 2n − m comparisons.…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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