## A Lower Bound for Parallel String Matching (1993)

Venue: | SIAM J. Comput |

Citations: | 25 - 13 self |

### BibTeX

@ARTICLE{Breslauer93alower,

author = {Dany Breslauer},

title = {A Lower Bound for Parallel String Matching},

journal = {SIAM J. Comput},

year = {1993},

volume = {21},

pages = {856--862}

}

### Years of Citing Articles

### OpenURL

### Abstract

This talk presents the derivation of an\Omega\Gamma/28 log m) lower bound on the number of rounds necessary for finding occurrences of a pattern string P [1::m] in a text string T [1::2m] in parallel using m comparisons in each round. The parallel complexity of the string matching problem using p processors for general alphabets follows. 1. Introduction Better and better parallel algorithms have been designed for string-matching. All are on CRCW-PRAM with the weakest form of simultaneous write conflict resolution: all processors which write into the same memory location must write the same value of 1. The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in [8, 17] and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algorithm. Unlike...

### Citations

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606 | A Fast String Searching Algorithm - Boyer, Moore - 1977 |

312 |
Approximate formulas for some functions of prime numbers
- Rosser, Schoenfeld
- 1962
(Show Context)
Citation Context ...e range 1 2 K i+1 : : : K i+1 that forces at most 4mK i log m K i+1 comparisons. Proof. The number of prime multiples of k i that satisfy 1 2 K i+1sk i+1sK i+1 is greater than K i+1 4K i log m . From =-=[15]-=-, the number of primes between 1 2 n and n is greater than 1 4 n log n . Also, let p; qsq m k i be relatively prime, and l; q be two different integers: 1sk ! lsm. The double condition l j k mod pk i ... |

47 |
Relations between concurrent-write models of parallel computation
- Fich, Ragde, et al.
- 1988
(Show Context)
Citation Context ...xed alphabet strings. Similarly, finding the maximum in the parallel decision tree model has the same lower bound [16], but for small integers the maximum can be found in constant time on a CRCW-PRAM =-=[7]-=-. 2. A lower bound for finding the period of a string and string matching Given a string S[1::m], we say that k is a period length of S if S[i + k] = S[i] for i = 1; : : : ; m \Gamma k. We call k the ... |

41 | Parallel construction of a suffix tree with applications - Apostolico, Iliopoulos, et al. - 1988 |

39 |
Optimal parallel algorithms for string matching
- Galil
- 1985
(Show Context)
Citation Context ... must write the same value of 1. The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in =-=[8, 17]-=- and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algori... |

29 |
Optimal parallel pattern matching in strings
- VISHKIN
- 1985
(Show Context)
Citation Context ... must write the same value of 1. The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in =-=[8, 17]-=- and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algori... |

28 | Time space optimal string matching - GALIL, SEIFERAS - 1983 |

25 |
Deterministic sampling - A new technique for fast pattern matching
- Vishkin
- 1991
(Show Context)
Citation Context ...ms have been designed: O(logm) time in [8, 17] and O(log log m) time in [4]. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin =-=[18]-=- developed an optimal O(log m) time algorithm. Unlike in the case of the other algorithms this time bound does not account for the preprocessing of the pattern: the preprocessing takes O( log 2 m log ... |

24 | A Time-Space Tradeoff for Sorting on Non-Oblivious Machines - Borodin, Kirkpatrick, et al. - 1981 |

12 | k one-way heads cannot do string matching - Jiang, Li - 1993 |

10 | Saving space in fast string-matching - GALIL, SEIFERAS - 1977 |

10 | Optimal parallel pattern matching - Vishkin - 1985 |

9 | String-matching cannot be done by a two-head oneway deterministic finite automaton - Li, Yesha - 1986 |

8 |
Parallelism in comparison models
- Valiant
- 1975
(Show Context)
Citation Context ...ely, the exact parallel complexity of string matching for general alphabets on the CRCW-PRAM is: \Theta(d m p e + log log d1+p=me 2p). Our model is similar to Valiant's parallel comparison tree model =-=[16]-=-. We assume the only access the algorithm has to the input strings is by comparisons which check whether two symbols are equal or not. The algorithm is allowed p comparisons in each round, after which... |

5 |
An optimal O(log log n) parallel string matching algorithm
- Breslauer, Galil
- 1990
(Show Context)
Citation Context ...The best CREW-PRAM algorithms are those obtained from the CRCW algorithms for a logarithmic loss of efficiency. Optimal algorithms have been designed: O(logm) time in [8, 17] and O(log log m) time in =-=[4]-=-. (An optimal algorithm is one with pt = O(n) where t is the time and p is the number of processors used.) Recently, Vishkin [18] developed an optimal O(log m) time algorithm. Unlike in the case of th... |

4 | String-Matching and Periods - Crochemore - 1989 |

4 | Two-way pattern matching - Crochemore, Perrin - 1989 |

4 | Lower bounds on string-matching - Li - 1984 |

2 | Parallel construction of a suffix tree with applications - Landau, Schieber, et al. - 1988 |

1 | A time-space tradeoff for sorting on non-oblivious machines - Kirkpatrick - 1979 |