## Simple Fast Parallel Hashing by Oblivious Execution (1994)

Venue: | AT&T Bell Laboratories |

Citations: | 4 - 2 self |

### BibTeX

@TECHREPORT{Gil94simplefast,

author = {Joseph Gil and Yossi Matias},

title = {Simple Fast Parallel Hashing by Oblivious Execution},

institution = {AT&T Bell Laboratories},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by "oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the near-logarithmic time level. The algorithm is simple and is sketched by the following: 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t := 1 to O(lg lg n) do (a) Allocate M t memory blocks, each of size K t . (b) Let each bucket select a block at random, and try to injectively map its keys into the block using a random linear function. Buckets that fail carry on to the next iteration. The crux of the algorithm is a careful a priori selection of the parameters M t and K t . The algorithm uses only O(lg lg...

### Citations

1693 | The Probabilistic Method - Alon, Spencer - 1992 |

674 | Universal classes of hash functions - Carter, Wegman - 1979 |

636 | An Introduction to Parallel Algorithms - JAJA - 1992 |

509 | Concrete Mathematics: A Foundation For Computer Science - Graham, Knuth, et al. - 1994 |

254 | Sorting and Searching, Volume 3 of The Art of Computer Programming - Knuth - 1973 |

217 | Storing a sparse table with O(1) worst case access time - Fredman, Komlós, et al. - 1984 |

202 |
General Purpose Parallel Architectures, Chapter 18 of Handbook of Theoretical
- Valiant
- 1990
(Show Context)
Citation Context ... obtain a lowcontention parallel hashing algorithm for the qrqw pram model [19]; this implies an efficient hashing algorithm on Valiant's bsp model, and hence on hypercube-type non-combining networks =-=[44]-=-. Acknowledgments We thank Martin Dietzfelbinger and Faith E. Fich for providing helpful comments. We also wish to thank Uzi Vishkin and Avi Wigderson for early discussions. Part of this research was ... |

127 | Dynamic perfect hashing: Upper and lower bounds - Dietzfelbinger, Karlin, et al. - 1994 |

116 | An O(log n) parallel connectivity algorithm - SHILOACH, VISHKIN - 1982 |

92 | On the power of two-point based sampling - Chor, Goldreich - 1989 |

86 | auf der Heide. Efficient PRAM simulation on a distributed memory machine - Karp, Luby, et al. - 1992 |

56 |
1988]. \Data structures and algorithms for approximate string matching
- Galil, Giancarlo
(Show Context)
Citation Context ...using the scheme of [39], the resulting time increase is O(lg n). By using the new scheme, the time increase is only O (lg lg n lg n). This is the case in the construction of suffix trees for strings =-=[2, 17]-=- and in the naming assignment procedure for substrings over large alphabets [17]. For other algorithms, the time increase in [39] was O(lg lg n) or O \Gamma (lg lg n) 2 \Delta , while our algorithm le... |

46 | Relations between concurrent-write models of parallel computation - Fich, Ragde, et al. - 1988 |

45 | On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications - Siegel - 1989 |

45 |
Towards a Theory of Nearly Constant Time Parallel Algorithms
- Gil, Matias, et al.
- 1991
(Show Context)
Citation Context ...implied by the lower bound of Beame and Hastad [4]. This lower bound holds even for randomized algorithms. (More recent results have found other, more involved, ways to circumvent these barriers; cf. =-=[38, 3, 26, 30]-=-.) We circumvent the obstacle of learning buckets sizes for the purpose of appropriate memory allocation by a technique of oblivious execution, sketched by Figure 1. 1. Partition the input set into bu... |

43 | Converting high probability into nearly-constant time - with applications to parallel hashing - Matias, Vishkin - 1991 |

42 | Optimal bounds for decision problems - Beame, Hastad - 1989 |

42 | The QRQW PRAM: Accounting for contention in parallel algorithms - Gibbons, Matias, et al. - 1994 |

39 | Doubly Logarithmic Communication Algorithms for Optical Communication Parallel Computers - Goldberg, Jerrum, et al. - 1994 |

38 | auf der Heide. A new universal class of hash functions and dynamic hashing in real time - Dietzfelbinger, Meyer - 1990 |

32 | A.: Data structures - Mehlhorn, Tsakalidis - 1990 |

30 | Efficient Low-Contention Parallel Algorithms - Gibbons, Matias, et al. - 1994 |

26 | A Universal Interconnection Pattern for Parallel Computers - Goldschlager - 1982 |

25 | On parallel hashing and integer sorting - Matias, Vishkin - 1990 |

24 | Improved Deterministic Parallel Integer Sorting - Bhatt, Diks, et al. - 1991 |

24 |
Polynomial hash functions are reliable
- Dietzfelbinger, Gil, et al.
- 1992
(Show Context)
Citation Context ... algorithms were given by Dietzfelbinger, Karlin, Mehlhorn, Meyer auf der Heide, Rohnert and Tarjan [12], Dietzfelbinger and Meyer auf der Heide [14], and by Dietzfelbinger, Gil, Matias and Pippenger =-=[11]-=-. In the parallel setting, Dietzfelbinger and Meyer auf der Heide [13] presented an algorithm for the dictionary problem. For each fixed ffls0, n arbitrary dictionary instructions (insert, delete, or ... |

19 | Fast Hashing on a PRAM -- Designing by Expectation - Gil, Matias - 1991 |

19 |
Optimal separations between concurrent-write parallel machines
- Boppana
- 1989
(Show Context)
Citation Context ...tions about the behavior of previous iterations. Remark The hashing result demonstrates the power of randomness in parallel computation on crcw machines with memory restricted to linear size. Boppana =-=[6]-=- considered the problem of Element Distinctness: given n integers, decide whether or not they are all distinct. He showed that solving Element Distinctness on an n-processor Priority machine with boun... |

18 | Optimal Parallel Bucket Sorting - Hagerup, “Towards - 1987 |

15 | Fast and reliable parallel hashing - Bast, Hagerup - 1991 |

11 | auf der Heide. An optimal parallel dictionary - Dietzfelbinger, Meyer - 1989 |

11 | Every ROBUST CRCW PRAM can Efficiently Simulate a PRIORITY PRAM - Hagerup, Radzik - 1990 |

11 | Data Structures and Algorithms: Sorting and Searching - Mehlhorn - 1984 |

10 | Incomparability in parallel computation - Grolmusz, Ragde - 1990 |

9 | Fast Load Balancing on a PRAM - Gil - 1991 |

9 |
New Simulations between CRCW PRAMs
- Chlebus, Diks, et al.
- 1989
(Show Context)
Citation Context ...ower are: the Priority ([29]) in which the lowest-numbered processor succeeds; the Arbitrary ([42]) in which one of the processors succeeds, and it is not known in advance which one; the Collision + (=-=[9]-=-) in which if different values are attempted to be written, a special collision symbol is written in the cell; the Collision ([15]) in which a special collision symbol is written in the cell; the Tole... |

8 | Optimal parallel approximation algorithms for prefix sums and integer sorting - Goodrich, Matias, et al. - 1994 |

5 | Fast and efficient simulations among CRCW PRAMs - Gil, Matias - 1994 |

3 | Parallel construction of a suffix tree - Apostolico, Iliopoulos, et al. - 1988 |

3 | Observations concerning synchronous parallel models of computation - Borodin, Hopcroft, et al. - 1980 |

3 | Simple fast parallel hashing - Gil, Matias - 1994 |

3 | Not all keys can be hashed in constant time - Gil, Heide, et al. - 1990 |

3 | An e ective load balancing policy for geometric decaying algorithms
- Gil, Matias
- 1991
(Show Context)
Citation Context ...y be established that the number of random bits in the load balancing algorithm can be reduced to O(lg p lg lg p). We finally remark that using load balancing in a more efficient way, as described in =-=[23]-=-, yields a faster work-efficient implementation. This simple technique is based on carefully choosing the appropriate times for invoking the load balancing procedure; it applies to any algorithm in wh... |

2 | Dynamic perfect hashing: Upper and lower bounds - Tarjan - 1994 |

2 | Designing algorithms by expectations - Gil, Matias - 1994 |