Open Access
Which patterns are hard to find
Richard Cole,Ramesh Hariharan,Ramesh Hariharan,Michael S. Paterson,Michael S. Paterson,Michael S. Paterson,Uri Zwick +6 more
- pp 59-68
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TLDR
The paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms and finds a lower bound of about (1 + &) .Abstract:
The paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + &) . n character comparisons is obtained. For general algorithms, a lower bound of about (1 + &) . n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 ,+ &)) n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding pattems with interesting combinatorial properties (these are the hard to find patterns). It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.read more
Citations
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Saving comparisons in the Crochemore-Perrin string matching algorithm
TL;DR: In this article, the first string-matching algorithm that makes fewer than 2n − m symbol comparisons and uses sub-linear space was presented, which is the state-of-the-art for string matching.
Journal ArticleDOI
Saving comparisons in the Crochemore-Perrin string-matching algorithm
TL;DR: These are the first string-matching algorithms that make fewer than 2n − m symbol comparisons and use sub-linear space.
Book ChapterDOI
Dictionary-Matching on Unbounded Alphabets: Uniform Length Dictionaries
TL;DR: Dictionary-matching is a generalization of the string- matching problem where one is looking simultaneously for all occurrences of several patterns in a single text.
Book ChapterDOI
Saving Comparisons in the Crochemore-Perrin String Matching Algorithm
TL;DR: This paper shows how to modify their algorithm to use fewer comparisons, an elegant linear-time constant-space string matching algorithm that makes at most 2n−m symbol comparison.
Book ChapterDOI
On the Exact Complexity of the String Prefix-Matching Problem (Extended Abstract)
TL;DR: In this article, the exact comparison complexity of the string prefix-matching problem in the deterministic sequential comparison model with equality tests was studied, and almost tight lower and upper bounds on the number of comparisons required in the worst case by on-line prefix matching algorithms for any fixed pattern and variable text were derived.
References
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Journal ArticleDOI
Fast Pattern Matching in Strings
TL;DR: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings, showing that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time.
Journal ArticleDOI
A fast string searching algorithm
TL;DR: The algorithm has the unusual property that, in most cases, not all of the first i.” in another string, are inspected.
Journal ArticleDOI
Speeding up two string-matching algorithms
Maxime Crochemore,Artur Czumaj,Leszek Gasieniec,Stefan Jarominek,Thierry Lecroq,Wojciech Plandowski,Wojciech Rytter +6 more
TL;DR: It is shown how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm), based on factor graphs for the reverse of the pattern.
Book ChapterDOI
Speeding Up Two String-Matching Algorithms
Maxime Crochemore,Thierry Lecroq,Artur Czumaj,Leszek Gasieniec,Stefan Jarominek,Wojciech Plandowski,Wojciech Rytter +6 more
TL;DR: It is shown how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm), based on factor graphs for the reverse of the pattern.
Journal ArticleDOI
On the exact complexity of string matching: lower bounds
Zvi Galil,Raffaele Giancarlo +1 more
TL;DR: This paper provides several lower bounds on the number of character comparisons that any string matching algorithm must perform in the worst case in order to find occurrences of a pattern string in a text string.