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Finding All Periods and Initial Palindromes of a String in Parallel

, 1991
"... An optimal O(log log n) time CRCWPRAM algorithm for computing all periods of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. This algorithm can be used to find all initial palindromes of a string in the same tim ..."
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Cited by 18 (10 self)
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An optimal O(log log n) time CRCWPRAM algorithm for computing all periods of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. This algorithm can be used to find all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We derive a lower bound for finding palindromes by a modification of a previously known lower bound for finding the period of a string [3]. When p processors are available the bounds become \Theta(d n p e + log log d1+p=ne 2p).
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.
Testing String Superprimitivity in Parallel
 Information Processing Letters
, 1992
"... A string w covers another string z if every symbol of z is within some occurrence of w in z. A string is called superprimitive if it is covered only by itself, and quasiperiodic if it is covered by some shorter string. This paper presents an O(log log n) time n log n log log n processor CRCW ..."
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Cited by 11 (1 self)
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A string w covers another string z if every symbol of z is within some occurrence of w in z. A string is called superprimitive if it is covered only by itself, and quasiperiodic if it is covered by some shorter string. This paper presents an O(log log n) time n log n log log n processor CRCWPRAM algorithm that tests if a string is superprimitive. The algorithm is the fastest possible with this number of processors over a general alphabet. 1 Introduction Quasiperiodicity, as defined by Apostolico and Ehrenfeucht [3], is an avoidable regularity of strings that is strongly related to other regularities such as periods and squares [12]. Apostolico, Farach and Iliopoulos [4] and Breslauer [7] gave lineartime sequential algorithms that tests if a string is superprimitive. Apostolico and Ehrenfeucht [3] presented an algorithm that finds all maximal quasiperiodic substrings of a string. This paper presents a parallel algorithm that tests if a string of length n is superprimitive i...
Efficient Comparison Based String Matching
, 1992
"... We study the exact number of symbol comparisons that are required to solve the string matching problem and present a family of efficient algorithms. Unlike previous string matching algorithms, the algorithms in this family do not "forget" results of comparisons, what makes their analysi ..."
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Cited by 10 (3 self)
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We study the exact number of symbol comparisons that are required to solve the string matching problem and present a family of efficient algorithms. Unlike previous string matching algorithms, the algorithms in this family do not "forget" results of comparisons, what makes their analysis much simpler. In particular, we give a lineartime algorithm that finds all occurrences of a pattern of length m in a text of length n in n+d 4 log m+2 m (n \Gamma m)e comparisons. The pattern preprocessing takes linear time and makes at most 2m comparisons. This algorithm establishes that, in general, searching for a long pattern is easier than searching for a short one. We also show that any algorithm in the family of the algorithms presented must make at least n + blog mcb n\Gammam m c symbol comparisons, for m = 2 k \Gamma 1 and any integer k 1.
Fast Parallel String PrefixMatching
 Theoret. Comput. Sci
, 1992
"... An O(log log m) time n log m log log m processor CRCWPRAM algorithm for the string prefixmatching problem over a general alphabet is presented. The algorithm can also be used to compute the KMP failure function in O(log log m) time on m log m log log m processors. These results improve on th ..."
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Cited by 6 (2 self)
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An O(log log m) time n log m log log m processor CRCWPRAM algorithm for the string prefixmatching problem over a general alphabet is presented. The algorithm can also be used to compute the KMP failure function in O(log log m) time on m log m log log m processors. These results improve on the running time of the best previous algorithm for both problems, which was O(log m), while preserving the same number of operations. 1 Introduction String matching is the problem of finding all occurrences of a short pattern string P[1::m] in a longer text string T [1::n]. The classical sequential algorithm of Knuth, Morris and Pratt [12] solves the string matching problem in time that is linear in the length of the input strings. The KnuthMorrisPratt [12] string matching algorithm can be easily generalized to find the longest pattern prefix that starts at each text position within the same time bound. We refer to this problem as string prefixmatching. In parallel, the string matching p...
Online and Dynamic Recognition of Squarefree Strings
"... Abstract. The online squarefree recognition problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. We present an efficient algorithm to solve this problem for strings over arbitrarily ordered alphabets. Its running time is O(n log n), ..."
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Abstract. The online squarefree recognition problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. We present an efficient algorithm to solve this problem for strings over arbitrarily ordered alphabets. Its running time is O(n log n), where n is the ending position of the first square, which matches the running times of the fastest known algorithms for the analogous offline problem. We also present a very simple algorithm for a dynamic version of the problem over general alphabets in which we are initially given a squarefree string, followed by a series of updates, and the objective is to determine after each update if the resulting string contains a square and if so, report it and stop. 1
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
A NEW STRING MATCHING ALGORITHM
, 2002
"... In this paper a new exact stringmatching algorithm with sublinear average case complexity has been presented. Unlike other sublinear stringmatching algorithms it never performs more than n text character comparisons while working on a text of length n. It requires only O(m þ s) extra preprocess ..."
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In this paper a new exact stringmatching algorithm with sublinear average case complexity has been presented. Unlike other sublinear stringmatching algorithms it never performs more than n text character comparisons while working on a text of length n. It requires only O(m þ s) extra preprocessing time and space, where m is the length of the pattern and s is the size of the alphabet.
Parallelism for Computational Molecular Biology
, 2000
"... The aim of this paper is to propose an analysis of existing works on parallel sequence comparison. Sequence comparison is one of the most common operation occurring in computational molecular biology. ..."
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The aim of this paper is to propose an analysis of existing works on parallel sequence comparison. Sequence comparison is one of the most common operation occurring in computational molecular biology.