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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.
Saving Comparisons in the CrochemorePerrin String Matching Algorithm
 IN PROC. OF 1ST EUROPEAN SYMP. ON ALGORITHMS
, 1992
"... Crochemore and Perrin discovered an elegant lineartime constantspace string matching algorithm that makes at most 2n \Gamma m symbol comparison. This paper shows how to modify their algorithm to use fewer comparisons. Given any fixed ffl ? 0, the modified algorithm takes linear time, uses constant ..."
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Cited by 9 (1 self)
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Crochemore and Perrin discovered an elegant lineartime constantspace string matching algorithm that makes at most 2n \Gamma m symbol comparison. This paper shows how to modify their algorithm to use fewer comparisons. Given any fixed ffl ? 0, the modified algorithm takes linear time, uses constant space and makes at most n+ b 1+ffl 2 (n \Gamma m)c comparisons. If O(log m) space is available, then the algorithm makes at most n + b 1 2 (n \Gamma m)c comparisons. The pattern preprocessing step also takes linear time and uses constant space. These are the first string matching algorithms that make fewer than 2n \Gamma m comparisons and use sublinear space.
The Zooming Method: A Recursive Approach to TimeSpace Efficient StringMatching
 Comput. Sci
, 1995
"... A new approach to timespace efficient stringmatching is presented. The method is flexible, its implementation depends whether or not the alphabet is linearly ordered. The only known lineartime constantspace algorithm for stringmatching over nonordered alphabets is the GalilSeiferas algorithm, s ..."
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Cited by 7 (5 self)
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A new approach to timespace efficient stringmatching is presented. The method is flexible, its implementation depends whether or not the alphabet is linearly ordered. The only known lineartime constantspace algorithm for stringmatching over nonordered alphabets is the GalilSeiferas algorithm, see [8, 6] which is rather complicated. The zooming method gives probably the simplest stringmatching algorithm working in constant space and linear time for nonordered alphabets. The novel feature of our algorithm is the application of the searching phase (which is usually simpler than preprocessing) in the preprocessing phase. The preprocessing has a recursive structure similar to selection in linear time, see [1]. For ordered alphabets the preprocessing part is much simpler, its basic component is a simple and wellknown algorithm for finding the maximal suffix, see [7]. Hence we demonstrate a new application of this algorithm, see also [5]. The idea of the zooming method was applied in [...
On the Comparison Complexity of the String PrefixMatching Problem
 IN PROC. 2ND EUROPEAN SYMPOSIUM ON ALGORITHMS, NUMBER 855 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1995
"... In this paper we study the exact comparison complexity of the string prefixmatching problem in the deterministic sequential comparison model with equality tests. We derive almost tight lower and upper bounds on the number of symbol comparisons required in the worst case by online prefixmatchi ..."
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Cited by 6 (0 self)
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In this paper we study the exact comparison complexity of the string prefixmatching problem in the deterministic sequential comparison model with equality tests. We derive almost tight lower and upper bounds on the number of symbol comparisons required in the worst case by online prefixmatching algorithms for any fixed pattern and variable text. Unlike previous results on the comparison complexity of stringmatching and prefixmatching algorithms, our bounds are almost tight for any particular pattern. We also consider the special case where the pattern and the text are the same string. This problem, which we call the string selfprefix problem, is similar to the pattern preprocessing step of the KnuthMorrisPratt stringmatching algorithm that is used in several comparison efficient stringmatching and prefixmatching algorithms, including in our new algorithm. We obtain roughly tight lower and upper bounds on the number of symbol comparisons required in the worst case...
ConstantSpace String Matching with Smaller Number of Comparisons: Sequential Sampling
, 1995
"... A new stringmatching algorithm working in constant space and linear time is presented. It is based on a powerful idea of sampling, originally introduced in parallel computations. The algorithm uses a sample S which consists of two positions inside the pattern P . First the positions of the sample S ..."
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Cited by 6 (3 self)
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A new stringmatching algorithm working in constant space and linear time is presented. It is based on a powerful idea of sampling, originally introduced in parallel computations. The algorithm uses a sample S which consists of two positions inside the pattern P . First the positions of the sample S are tested against the corresponding positions of the text T , then a version of KnuthMorrisPratt algorithm is applied. This gives the simplest known stringmatching algorithm which works in constant space and linear time and which does not use any linear order of the alphabet. A rened version of the algorithm gives the fastest (in the sense of number of comparisons) known algorithm for stringmatching in constant space. It makes (1 + ")n +O( n m ) symbol comparisons. This improves substantially the result of [3], where a ( 3 2 + ")n comparisons constant space algorithm was designed. 1 Introduction Assume we are given two strings: a pattern P of length m and a text T of length n. The ...
ConstantSpace StringMatching in Sublinear Average Time (Extended Abstract)
"... ) Maxime Crochemore Universit`e de MarnelaVall`ee Leszek Gasieniec y MaxPlanck Institut fur Informatik Wojciech Rytter z Warsaw University and University of Liverpool Abstract Given two strings: pattern P of length m and text T of length n. The stringmatching problem is to find all o ..."
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Cited by 2 (0 self)
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) Maxime Crochemore Universit`e de MarnelaVall`ee Leszek Gasieniec y MaxPlanck Institut fur Informatik Wojciech Rytter z Warsaw University and University of Liverpool Abstract Given two strings: pattern P of length m and text T of length n. The stringmatching problem is to find all occurrences of the pattern P in the text T . We present a simple stringmatching algorithms which works in average o(n) time with constant additional space for onedimensional texts and twodimensional arrays. This is the first attempt to the smallspace stringmatching problem in which sublinear time algorithms are delivered. More precisely we show that all occurrences of one or twodimensional patterns can be found in O( n r ) average time with constant memory, where r is the repetition size (size of the longest repeated subword) of P . Institut Gaspard Monge, Universit`e de MarnelaVall`ee, France (mac@univmlv.fr). y MaxPlanck Institut fur Informatik, Im Stadtwald, D6612...
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