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Some applications of Rabin's fingerprinting method
 Sequences II: Methods in Communications, Security, and Computer Science
, 1993
"... Rabin's fingerprinting scheme is based on arithmetic modulo an irreducible polynomial with coefficients in Z 2 . This paper presents an implementation and several applications of this scheme that take considerable advantage of its algebraic properties. 1 Introduction Fingerprints are short tags for ..."
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Cited by 89 (3 self)
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Rabin's fingerprinting scheme is based on arithmetic modulo an irreducible polynomial with coefficients in Z 2 . This paper presents an implementation and several applications of this scheme that take considerable advantage of its algebraic properties. 1 Introduction Fingerprints are short tags for larger objects. They have the property that if two fingerprints are different then the corresponding objects are certainly different and there is only a small probability that two different objects have the same fingerprint. (The latter event is called a collision.) More precisely, a fingerprinting scheme is a certain collection of functions F = n f :\Omega ! f0; 1g k o , where\Omega is the set of all possible objects of interest and k is the length of the fingerprint, such that, for any choice of a fixed set S ae\Omega of n distinct objects, if f is chosen uniformly at random in F , then with high probability jf(S)j = jSj : In other words, if an adversary chooses a set S ae\Ome...
An Optimal O(log log n) Time Parallel Algorithm for Detecting all Squares in a String
, 1995
"... An optimal O(log log n) time concurrentread concurrentwrite parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm. When p processors are available the bounds become \Theta(d n ..."
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Cited by 11 (6 self)
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An optimal O(log log n) time concurrentread concurrentwrite parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm. When p processors are available the bounds become \Theta(d n log n p e + log log d1+p=ne 2p). The algorithm uses an optimal parallel stringmatching algorithm together with periodicity properties to locate the squares within the input string.
Efficient String Algorithmics
, 1992
"... Problems involving strings arise in many areas of computer science and have numerous practical applications. We consider several problems from a theoretical perspective and provide efficient algorithms and lower bounds for these problems in sequential and parallel models of computation. In the sequ ..."
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Cited by 8 (6 self)
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Problems involving strings arise in many areas of computer science and have numerous practical applications. We consider several problems from a theoretical perspective and provide efficient algorithms and lower bounds for these problems in sequential and parallel models of computation. In the sequential setting, we present new algorithms for the string matching problem improving the previous bounds on the number of comparisons performed by such algorithms. In parallel computation, we present tight algorithms and lower bounds for the string matching problem, for finding the periods of a string, for detecting squares and for finding initial palindromes.
Finding maximal quasiperiodicities in strings
 In Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching (CPM
, 2000
"... Abstract. Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic substring and gave an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log 2 n). In this paper we give an algorithm that finds all maximal quasiperiodic substrings in a str ..."
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Cited by 7 (3 self)
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Abstract. Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic substring and gave an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log 2 n). In this paper we give an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log n) andspaceO(n). Our algorithm uses the suffix tree as the fundamental data structure combined with efficient methods for merging and performing multiple searches in search trees. Besides finding all maximal quasiperiodic substrings, our algorithm also marks the nodes in the suffix tree that have a superprimitive pathlabel. 1
String Pattern Matching For A Deluge Survival Kit
, 2000
"... String Pattern Matching concerns itself with algorithmic and combinatorial issues related to matching and searching on linearly arranged sequences of symbols, arguably the simplest possible discrete structures. As unprecedented volumes of sequence data are amassed, disseminated and shared at an incr ..."
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Cited by 5 (1 self)
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String Pattern Matching concerns itself with algorithmic and combinatorial issues related to matching and searching on linearly arranged sequences of symbols, arguably the simplest possible discrete structures. As unprecedented volumes of sequence data are amassed, disseminated and shared at an increasing pace, effective access to, and manipulation of such data depend crucially on the efficiency with which strings are structured, compressed, transmitted, stored, searched and retrieved. This paper samples from this perspective, and with the authors' own bias, a rich arsenal of ideas and techniques developed in more than three decades of history.
On Finding Duplication in Strings and Software
 Journal of Algorithms
, 1993
"... This paper investigates finding duplication within a string. The results are phrased in terms of maximal matches, which are pairs of substrings that match but for which the match cannot be extended to the left or right in the input. An algorithm is given to find all maximal exact matches over a thre ..."
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Cited by 4 (1 self)
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This paper investigates finding duplication within a string. The results are phrased in terms of maximal matches, which are pairs of substrings that match but for which the match cannot be extended to the left or right in the input. An algorithm is given to find all maximal exact matches over a threshold length. For a finite alphabet S, it runs in time O(nlog ï S ï + m), where n is the input length and m is the number of matches reported. The algorithm has been implemented and has been used as the basis of a program for finding code duplication in large software systems. February 15, On Finding Duplication in Strings and Software Brenda S. Baker AT&T Bell Laboratories Murray Hill, New Jersey 07974 1. Introduction This paper describes an algorithm for finding duplication in strings and its application to finding duplication in software. The basic problem is to find all maximal matches, which are pairs of substrings that match but for which the match cannot be extended to the left o...
Efficient String Matching on Coded Texts
 In Proceedings of Combinatorial Pattern Matching, 6th Annual Symposium (CPM'95
, 1994
"... The so called "four Russians technique" is often used to speed up algorithms by encoding several data items in a single memory cell. Given a sequence of n symbols over a constant size alphabet, one can encode the sequence into O(n=) memory cells in O(log ) time using n= log processors. This paper ..."
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Cited by 2 (1 self)
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The so called "four Russians technique" is often used to speed up algorithms by encoding several data items in a single memory cell. Given a sequence of n symbols over a constant size alphabet, one can encode the sequence into O(n=) memory cells in O(log ) time using n= log processors. This paper presents an efficient CRCWPRAM stringmatching algorithm for coded texts that takes O(log log(m=)) time 1 making only O(n=) operations, an improvement by a factor of = O(logn) on the number of operations used in previous algorithms. Using this stringmatching algorithm one can test if a string is squarefree and find all palindromes in a string in O(log log n) time using n= log log n processors. 1 Introduction In the stringmatching problem one is searching for occurrences of a pattern string P[1::m] in a text string T [1::n]. There exist several O(n + m) time sequential stringmatching algorithms that are used in a large variety of applications. Galil [23] published the first efficient...
On the Complexity of Computing the Order of Repetition of a String
, 1998
"... We show a simple O(n log n) time algorithm computing the order of repetition in a string. A parallel version of the algorithm works in O(log ..."
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We show a simple O(n log n) time algorithm computing the order of repetition in a string. A parallel version of the algorithm works in O(log
Detecting all Squares in a String ∗
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS