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108
Optimal Parallel Algorithms for Periods, Palindromes and Squares (Extended Abstract)
, 1992
"... ) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and TelAviv University Summary of results Optimal concurrentread concurrentwrite parallel algorithms for two problems are presented: ffl Finding all the pe ..."
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Cited by 32 (13 self)
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) Alberto Apostolico Purdue University and Universit`a di Padova Dany Breslauer yyz Columbia University Zvi Galil z Columbia University and TelAviv University Summary of results Optimal concurrentread concurrentwrite parallel algorithms for two problems are presented: ffl Finding all the periods of a string. The period of a string can be computed by previous efficient parallel algorithms only if it is shorter than half of the length of the string. Our new algorithm computes all the periods in optimal O(log log n) time, even if they are longer. The algorithm can be used to compute all initial palindromes of a string within the same bounds. ffl Testing if a string is squarefree. We present an optimal O(log log n) time algorithm for testing if a string is squarefree, improving the previous bound of O(log n) given by Apostolico [1] and Crochemore and Rytter [12]. We show matching lower bounds for the optimal parallel algorithms that solve the problems above on a general alphab...
Embeddings of graph braid and surface groups in rightangled Artin groups and braid groups
, 2008
"... ..."
Optimal Superprimitivity Testing for Strings
, 1991
"... A string w covers another string z if every position of z is within some occurrence of in z. ..."
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Cited by 28 (5 self)
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A string w covers another string z if every position of z is within some occurrence of in z.
An optimal O(log log n) time parallel string matching algorithm
 SIAM J. COMPUT
, 1990
"... An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V]. ..."
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Cited by 27 (11 self)
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An optimal O(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].
Periodicity on Partial Words
 Computers and Mathematics with Applications 47
, 2004
"... Codes play an important role in the study of combinatorics on words. Recently, we introduced pcodes that play a role in the study of combinatorics on partial words. Partial words are strings over a finite alphabet that may contain a number of “do not know ” symbols. In this paper, the theory of code ..."
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Cited by 22 (8 self)
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Codes play an important role in the study of combinatorics on words. Recently, we introduced pcodes that play a role in the study of combinatorics on partial words. Partial words are strings over a finite alphabet that may contain a number of “do not know ” symbols. In this paper, the theory of codes of words is revisited starting from pcodes of partial words. We present some important properties of pcodes. We give several equivalent definitions of pcodes and the monoids they generate. We investigate in particular the Defect Theorem for partial words. We describe an algorithm to test whether or not a finite set of partial words is a pcode. We also discuss twoelement pcodes, complete pcodes, maximal pcodes, and the class of circular pcodes. A World Wide Web server interface has been established at
Implicit function theorem over free groups and genus problem
 AMS/IP Studies in Advanced Mathematics
"... groups ..."
Optimal Parallel Suffix Tree Construction
, 1997
"... An O(m)work, O(m)space, O(log m)time CREWPRAM algorithm for constructing the suffix tree of a string s of length m drawn from any fixed alphabet set is obtained. This is the first known work and space optimal parallel algorithm for this problem. It can be generalized to a string s drawn fr ..."
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Cited by 18 (1 self)
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An O(m)work, O(m)space, O(log m)time CREWPRAM algorithm for constructing the suffix tree of a string s of length m drawn from any fixed alphabet set is obtained. This is the first known work and space optimal parallel algorithm for this problem. It can be generalized to a string s drawn from any general alphabet set to perform in O(log m) time and O(m log j\Sigmaj) work and space, after the characters in s have been sorted alphabetically, where j\Sigmaj is the number of distinct characters in s. In this case too, the algorithm is workoptimal.
Reconstructing Strings from Substrings in Rounds
 In Proc. 36th Symposium on Foundation of Computer Science (FOCS 95
, 1995
"... We establish a variety of combinatorial bounds on the tradeoffs inherent in reconstructing strings using few rounds of a given number of substring queries per round. These results lead us to propose a new approach to sequencing by hybridization (SBH), which uses interaction to dramatically reduce th ..."
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Cited by 17 (2 self)
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We establish a variety of combinatorial bounds on the tradeoffs inherent in reconstructing strings using few rounds of a given number of substring queries per round. These results lead us to propose a new approach to sequencing by hybridization (SBH), which uses interaction to dramatically reduce the number of oligonucleotides used for de novo sequencing of large DNA fragments, while preserving the parallelism which is the primary advantage of SBH. 1 Introduction Sequencing by hybridization (SBH) [4, 11] is a new and promising approach to DNA sequencing which offers the potential of reduced cost and higher throughput over traditional gelbased approaches. In this paper, we propose a new approach to sequencing by hybridization which permits the sequencing of arbitrarily large fragments without the inherently exponential chip area of SBH, while retaining the massive parallelism which is the primary advantage of the technique. We establish the potential of our technique through both ana...
Computing the Covers of a String in Linear Time
, 1994
"... this paper we characterize all the covers of x in terms of an easily computed normal form for x. The characterization theorem then gives rise to a simple recursive algorithm which computes all the covers of x in time \Theta(n). By avoiding unnecessary checks, this algorithm appears to execute more q ..."
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Cited by 16 (2 self)
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this paper we characterize all the covers of x in terms of an easily computed normal form for x. The characterization theorem then gives rise to a simple recursive algorithm which computes all the covers of x in time \Theta(n). By avoiding unnecessary checks, this algorithm appears to execute more quickly than that given in [2]. Let x denote a string of length n = jxj 0; in particular, let ffl denote the empty string of zero length. For any nonempty string x, let k 1 be the greatest integer such that (1:1) x = (v