R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 248--258, Palo Alto, CA, November 3--5, 1993. IEEE Computer Society Press, Los Alamitos, CA.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....parallel prefix matching algorithm. Prefix matching algorithms have also been used in the sequential two dimensional pattern matching algorithms of Amir, Benson and Farach [2] and Galil and Park [25] and in an early version of the parallel two dimensional pattern matching algorithm of Cole et al. [11]. In this paper we study the exact number of comparisons performed by deterministic sequential prefix matching algorithms that have access to the input strings by pairwise symbol comparisons that test for equality. This work was motivated by recent interest in the exact comparison complexity of ....

R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proc. 34th IEEE Symp. on Foundations of Computer Science, pages 248--258, 1993. 37

....bound for string matching due to Breslauer and Galil [7] However, the lower bound is applied only to preprocessing of the pattern and the searching phase can be faster than O(log log m) time as in string matching. Unlike string matching where an optimal constant time searching phase was obtained [8], we prove an Omega (ff(m) lower bound for any linear work searching phase. Therefore our algorithm is work time optimal in both preprocessing and text search. As in the exact complexity of sequential computation, the Omega (ff(m) lower bound shows that prefix matching is harder than string ....

....log r. With log 2 r processors for each block, construct a covering in constant time. 2. Build BT 2 (r= log r) a complete binary tree with r= log r leaves. For every level 0 i log r, find survivors (at most one for each node of BT 2 (r= log r) by DS s in constant time with r processors [18, 8]. In every level build a level covering in constant time with r processors. 3. Construct a common covering from log r coverings in step 2. With log 2 r processors for each candidate, we can construct the common covering in constant time. 4. Combine the covering from step 1 and the covering ....

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R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park and W. Rytter, Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions, Proc. 34th IEEE Symp. Found. Computer Science, 1993.

....development of two dimensional periodicity [3] Two dimensional periodicity turned out to be the most important tool in two dimensional matching. Its development led to an alphabet independent two dimensional matching algorithm [6, 4, 18] and to optimal parallel two dimensional matching algorithms [5, 13]. Much progress has been made with dictionary matching as well. In the traditional pattern matching model a single pattern is sought in a single text. Dictionary matching allows preprocessing of a (possibly vast) dictionary of patterns. Subsequently, appearances of dictionary patterns in various ....

R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Harihan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. Proc. 34th IEEE FOCS, pages 248--258, 1993.

....a linear time (hence, optimal) algorithm for dictionary matching by generalizing the finite automaton construction in [19] to a set of strings. In the mid eighties, Galil [12] and Vishkin [27] designed the first work optimal string matching algorithms, which have since been extended significantly [28, 13, 9]. However, a work optimal algorithm for dictionary matching has remained elusive. As in the case of [19] the finite automaton based approach of [3] is inherently sequential. Recent progress on parallel dictionary matching [4, 5, 18, 22] based on alternate techniques has only yielded suboptimal ....

R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, K. Park, S. Muthukrishnan, H. Ramesh, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. Proc. of the 34th IEEE Annual Symp. on Foundation of Computer Science, pages 248-- 258, 1993.

....within the same time bound. This fact was first observed by Main and Lorentz [18] who used the generalized algorithm to find repetitions in strings. We refer to this problem as the string prefix matching problem. Prefix matching algorithms have also been used in two dimensional matching algorithms [1, 12, 15]. Formally, the output of the string prefix matching problem is an integer array Phi[1: n] 0 Phi[t] min(m; n Gamma t 1) such that for each text position t, T [t: t Phi[t] Gamma 1] P[1: Phi[t] and if Phi[t] m and t Phi[t] n, then T [t Phi[t] 6= P [ Phi[t] 1] In ....

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proc. 34th IEEE Symp. on Foundations of Computer Science, pages 248--258, 1993.

....in O(log log m) still with linear total work. They also showed (Breslauer and Galil, 1992) that this cannot be improved in the parallel comparison tree model. As we also prove in Chapter 6, this bound is the best possible on the Priority CRCW PRAM, assuming the PRAM memory is finite. Recently Cole et al. 1993) gave a new algorithm that after an O(log log m) time O(m) work preprocessing of the pattern, solves string matching in constant time on the n processor CRCW PRAM. They also gave a constant time randomized CRCW PRAM algorithm for string matching. All the algorithms mentioned above were designed ....

....T is 2 good, and when P is nonperiodic, T must be finally m=2 good. The lower bound of Breslauer and Galil (1992) as well as the lower bound presented in Chapter 6, indicate difficulty of computing the period very fast. In order to design a constant time randomized string matching algorithm Cole et al. 1993) relaxed the notion of periodicity and invented the idea of pseudo period. Given a string x with the period p, a pseudo period of x is any number q that divides p. Note that both 1 and p are pseudo periods of x, and if p is prime then q 2 f1; pg. We say we compute a pseudo period q of P if we ....

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Cole, R., Crochemore, M., Galil, Z., G¸asieniec, L., Hariharan, R., Muthukrishnan, S., Park, K., and Rytter, W. (1993), "Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions, " In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 248--258.

....they have been considered separately in the literature and they have different complexities. In this abstract we only discuss the first four problems. For all these eight problems there are wt optimal algorithms known on the CRCW PRAM : linear work and constant time for Problems 1 [15] and 3 [12]; linear work and O(log log n) time for Problems 2 [6] 4 [12] 5 [4] 6 [13] 8 [4] O(n log n) work and O(log log n) time for Problem 7 [3] The Omega Gammae 4 log n) lower bounds for the time follow from [7] The Omega Gamma n log n) lower bound for the work of Problem 7 follows from [23] A ....

....they have different complexities. In this abstract we only discuss the first four problems. For all these eight problems there are wt optimal algorithms known on the CRCW PRAM : linear work and constant time for Problems 1 [15] and 3 [12] linear work and O(log log n) time for Problems 2 [6] 4 [12], 5 [4] 6 [13] 8 [4] O(n log n) work and O(log log n) time for Problem 7 [3] The Omega Gammae 4 log n) lower bounds for the time follow from [7] The Omega Gamma n log n) lower bound for the work of Problem 7 follows from [23] A logarithmic lower bound for all these problems on the ....

[Article contains additional citation context not shown here]

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Hariharan, S. Muthukrishnan, K. Park and W. Rytter, Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions, Proc. 34th IEEE Symp. Found. Computer Science, 1993, 248--258.

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R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 248--258, Palo Alto, CA, November 3--5, 1993. IEEE Computer Society Press, Los Alamitos, CA.

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R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park and W. Rytter. Optimally Fast Parallel Algorithms for Preprocessing and Pattern Matching in One and Two Dimensions. In Proc. 34th IEEE Symp. on Foundations of Computer Science, pages 248--258, 1993.

....witness table (defined later) Let Sigma be the underlying alphabet. In two dimensions there are two approaches to compute this table efficiently: use the suffix trees (see [2] which is a factor log j Sigmaj slower than linear time, and the linear time alphabet independent algorithms of [9] and [6]. The alphabet independent algorithms are extremely complicated. They would be even more complicated in three dimensions. On the other hand if Sigma is large then we can replace log j Sigmaj by log m. We show a simple approach through the dictionary of basic factors (DBF, in short) This is a ....

....also given in [3] an alphabet independent searching in logM time with O(M= log(M ) processors of a CREW PRAM. We refer to the latter algorithm as the algorithm ABF . The algorithm ABF needs only the witness table from the preprocessing phase. An O(1) time optimal algorithm was given recently in [6], however it needs additional data structure from the preprocessing phase: so called deterministic sample. The basic precomputed data structure needed in our algorithm is (similarly as in the algorithm ABF) the witness table W IT . The entries of W IT correspond to vectors (potential periods) The ....

R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park, W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. FOCS'93.

....A, then by the definition of DS we can eliminate all other candidates in an m=2 block of the text. This method was used in a constanttime optimal text search [8] Very recently, it was also used in a constant time two constant time randomized parallel string matching 3 dimensional text search [5]. However, the optimal algorithm suggested by Vishkin and used in [8] for computing DS was very expensive, taking O(log 2 m= log log m) time. This resulted in two best algorithms for string matching: an optimal O(log log m) time algorithm for the entire problem [2] for which also ....

R. Cole, M. Crochemore, Z. Galil, L. Gasieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter, Optimally fast parallel algorithms for preprocessing and pattern matching in one constant-time randomized parallel string matching 11 and two dimensions, Proc. 34th IEEE Symp. Found. Computer Science, 1993, 248--258.

....1; Gamma 1. Vishkin [38] suggested the duel method to eliminate potential occurrences efficiently. His method, which is described next, has been used in all efficient parallel string matching algorithms afterward as well as in sequential and parallel two dimensional matching algorithms [1, 13, 17, 25]. The idea in duels is that if there are two potential occurrence of the pattern at positions p and q of the text, such that 0 q Gamma p , then since P [W P q Gammap ] 6= P [W P q Gammap Gamma (q Gamma p) the text symbol T [p W P q Gammap Gamma 1] can not be equal both to P ....

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proc. 34th IEEE Symp. on Foundations of Computer Science, pages 248--258, 1993.

....arbitrary alphabets, where m is the pattern length. Breslauer and Galil [4] designed an optimal algorithm running in time O(log log m) and proved in [5] a matching lower bound. More references to the literature on pattern matching on PRAMs can be found in the book [12] by J aJ a. Recently, in [7, 8], a constant time CRCW PRAM algorithm finding all occurrences of a pattern in a text has been developed, after a deterministic O(log log m) preprocessing phase on the pattern. These two papers also include a constant expected time randomized algorithm to preprocess the pattern. Optimal ....

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R.Hariharan, S. Muthukrishnan, K. Park and W. Rytter, Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions, in Proc. 34th Annual IEEE Symposium on Foundations of Computer Science, pp. 248-258, 1993.

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R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Harihan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. Proc. 34th IEEE FOCS, pages 248--258, 1993.

No context found.

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 248--258, 1993.

No context found.

R. Cole, M. Crochemore, Z. Galil, L. G¸asieniec, R. Hariharan, S. Muthukrishnan, K. Park and W. Rytter, Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions, Proc. 34th IEEE FOCS'93, p.248-258.

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