## Retrieval of scattered information by EREW, CREW, and CRCW PRAMs (1992)

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Venue: | In Proc. 3rd Scand. Workshop on Alg. Theory |

Citations: | 5 - 1 self |

### BibTeX

@INPROCEEDINGS{Fich92retrievalof,

author = {Faith Fich and Prabhakar Ragde},

title = {Retrieval of scattered information by EREW, CREW, and CRCW PRAMs},

booktitle = {In Proc. 3rd Scand. Workshop on Alg. Theory},

year = {1992},

pages = {pages}

}

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### Abstract

Abstract. The k-compaction problem arises when k out of n cells in an array are non-empty and the contents of these cells must be moved to the first k locations in the array. Parallel algorithms for k-compaction have obvious applications in processor allocation and load balancing; k-compaction is also an important subroutine in many recently developed parallel algorithms. We show that any EREW PRAM that solves the k-compaction problem requires Ω ( √ log n) time, even if the number of processors is arbitrarily large and k = 2. On the CREW PRAM, we show that every n-processor algorithm for k-compaction problem requires Ω(log log n) time, even if k = 2. Finally, we show that O(log k) time can be achieved on the ROBUST PRAM, a very weak CRCW PRAM model.

### Citations

522 | Graphs and Hypergraphs - Berge - 1973 |

312 |
Approximate formulas for some functions of prime numbers
- Rosser, Schoenfeld
- 1962
(Show Context)
Citation Context ...roup to their appropriate places in the answer. Thus it suffices to solve this smaller instance of k-compaction. There are more than 0.6q/ ln q prime numbers in the interval [q, 2q] for q ≥ 20.5 (see =-=[19]-=-). The number l has been chosen so that 0.6n (k−1)/l / ln � n (k−1)/l� ≥ l, for n sufficiently large. Therefore there are at least l prime numbers between n (k−1)/l and 2n (k−1)/l . Let p1, . . . , pl... |

289 | Parallel merge sort
- Cole
- 1988
(Show Context)
Citation Context ...k) steps using the algorithm of Lemma 4.1. Next, all but one copy of each nonzero value in these k O(1) cells are set to 0. This can be done in O(log k) steps using Cole’s CREW PRAM sorting algorithm =-=[4]-=-. Since the number of cells is also in O(n), there is a sufficient number of processors available. Finally, the k-compaction algorithm of Lemma 3.3, is applied to these cells to obtain the solution of... |

43 | On parallel searching
- Snir
- 1985
(Show Context)
Citation Context ...n Boolean inputs: Beame, Kik and Kuty̷lowski [2] show that the problem of broadcasting one value to n processors requires Θ(log n) time. Snir’s lower bound on searching a sorted table on an EREW PRAM =-=[22]-=- requires a large input domain due to the use of Ramsey theory. The ROBUST PRAM is a very weak CRCW PRAM [17], in which the result of a simultaneous write might be any value. An algorithm for this mod... |

32 |
The parallel simplicity of compaction and chaining
- Ragde
- 1990
(Show Context)
Citation Context ...cell, an arbitrary processor succeeds. (The terminology is from [8]). A weaker concurrent-read concurrent-write model is the COMMON PRAM, in which simultaneous writes must be of the same value. Ragde =-=[20]-=- gave a kcompaction algorithm and matching lower bound of Θ(log k/ log log n) for the COMMON PRAM using n processors. The immediate utility of this result was in the development of very fast randomize... |

25 | On parallel hashing and integer sorting
- Matias, Vishkin
- 1991
(Show Context)
Citation Context ...ependent instances of problems are worked on simultaneously by a fast algorithm with a low probability of failure, the failures can be gathered up by compaction and dealt with quickly. Papers such as =-=[1, 9, 10, 12, 14, 15, 18]-=- used compaction or approximate compaction as an essential subroutine in algorithms for space allocation, estimation, sorting, PRAM simulation, generation of random permutations, and computational geo... |

23 |
Using approximation algorithms to design parallel algorithms that may ignore processor allocation
- Goodrich
- 1991
(Show Context)
Citation Context ...ependent instances of problems are worked on simultaneously by a fast algorithm with a low probability of failure, the failures can be gathered up by compaction and dealt with quickly. Papers such as =-=[1, 9, 10, 12, 14, 15, 18]-=- used compaction or approximate compaction as an essential subroutine in algorithms for space allocation, estimation, sorting, PRAM simulation, generation of random permutations, and computational geo... |

19 |
Fast hashing on a PRAM|Designing by expectation
- Gil, Matias
- 1991
(Show Context)
Citation Context ...ependent instances of problems are worked on simultaneously by a fast algorithm with a low probability of failure, the failures can be gathered up by compaction and dealt with quickly. Papers such as =-=[1, 9, 10, 12, 14, 15, 18]-=- used compaction or approximate compaction as an essential subroutine in algorithms for space allocation, estimation, sorting, PRAM simulation, generation of random permutations, and computational geo... |

17 |
Fast and reliable parallel hashing
- Bast, Hagerup
- 1991
(Show Context)
Citation Context |

17 |
The Log-Star Revolution
- Hagerup
- 1992
(Show Context)
Citation Context |

11 |
Exact Time Bounds for Computing Boolean Functions on PRAMs Without Simultaneous Writes
- Dietzfelbinger, Kutylowski, et al.
(Show Context)
Citation Context ...)−1 = j ′′ +c(t+1)− 1 mod m so that, after step t+1, Ci,j ′′ contains the value Last([aj ′′, . . . , aj ′′ +c(t+1)−1]), whether or not Pi,j wrote. If T ≥ logb m + 1.34, F2T +1 ≥ m. (See, for example, =-=[6]-=-.) Thus, after T steps, each cell Ci,j contains (k, ak), where ak is the last element in the sequence [aj, aj+1, . . . , am, a1, . . . , aj−1] that is different from 0, if such an element exists. Othe... |

11 |
Every ROBUST CRCW PRAM can Efficiently Simulate a PRIORITY PRAM
- Hagerup, Radzik
- 1990
(Show Context)
Citation Context ...ors requires Θ(log n) time. Snir’s lower bound on searching a sorted table on an EREW PRAM [22] requires a large input domain due to the use of Ramsey theory. The ROBUST PRAM is a very weak CRCW PRAM =-=[17]-=-, in which the result of a simultaneous write might be any value. An algorithm for this model must be correct even if an adversary decides the outcome of every simultaneous write. Every other CRCW PRA... |

7 |
Counting and Packing in Parallel
- Gil, Rudolph
(Show Context)
Citation Context ...tial fragment of the array. This problem has been considered in many contexts; for instance, this is a natural subproblem to consider in the context of processor or task reallocation. Gil and Rudolph =-=[11]-=- gave a deterministic algorithm to solve this problem in time O(log k) on a concurrent-read concurrent-write parallel random access machine (CRCW PRAM) using n processors. Rudolph and Steiger [21] gav... |

7 |
Parallel retrieval of scattered information
- Hagerup, Nowak
- 1989
(Show Context)
Citation Context ...el random access machine (CRCW PRAM) using n processors. Rudolph and Steiger [21] gave a probabilistic algorithm running in time O(log k) (with high probability) using k processors. Hagerup and Nowak =-=[16]-=- gave a probabilistic algorithm running in time O(log k/ log log k) using n processors. All of these algorithms use an ARBITRARY CRCW PRAM, with the property that when several processors simultaneousl... |

5 |
Dwork C, Reischuk R: Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes
- Cook
- 1986
(Show Context)
Citation Context ...the subroutine. To be concrete, let m = √ n and suppose that cells Ci,1, . . . , Ci,m initially contain the values a1, . . . , am. The subroutine is based on the algorithm of Cook, Dwork and Reischuk =-=[5]-=- for computing the OR of m Boolean variables. We define a function Last that identifies the last occurrence of a nonzero value in a sequence, if one exists. More precisely, Last([x1, . . . , xv]) = 0 ... |

3 |
Wigderson: Relations Between Concurrent-Write Models of Parallel Computation
- Fich, Ragde, et al.
- 1988
(Show Context)
Citation Context .... All of these algorithms use an ARBITRARY CRCW PRAM, with the property that when several processors simultaneously write into the same cell, an arbitrary processor succeeds. (The terminology is from =-=[8]-=-). A weaker concurrent-read concurrent-write model is the COMMON PRAM, in which simultaneous writes must be of the same value. Ragde [20] gave a kcompaction algorithm and matching lower bound of Θ(log... |

3 |
Subset Selection in Parallel
- Rudolph, Steiger
(Show Context)
Citation Context ...lph [11] gave a deterministic algorithm to solve this problem in time O(log k) on a concurrent-read concurrent-write parallel random access machine (CRCW PRAM) using n processors. Rudolph and Steiger =-=[21]-=- gave a probabilistic algorithm running in time O(log k) (with high probability) using k processors. Hagerup and Nowak [16] gave a probabilistic algorithm running in time O(log k/ log log k) using n p... |

2 |
Fast and Optimal Simulations between CRCW PRAMs
- Hagerup
- 1992
(Show Context)
Citation Context |

1 |
Kik and M. Kuty/lowski: Information broadcasting by Exclusive Read PRAMs
- Beame, M
(Show Context)
Citation Context ...or this model, the k-compaction problem requires Ω( √ log n) time, even when k = 2. There are very few lower bounds on the EREW PRAM for problems defined on Boolean inputs: Beame, Kik and Kuty̷lowski =-=[2]-=- show that the problem of broadcasting one value to n processors requires Θ(log n) time. Snir’s lower bound on searching a sorted table on an EREW PRAM [22] requires a large input domain due to the us... |

1 |
Towards a Theory of Nearly Constant Parallel Time Algorithms
- Gil, Matias, et al.
- 1991
(Show Context)
Citation Context |