### Abstract

For a wide class of problems, we obtain lower bounds for algorithms executed on certain parallel processors. These bounds show that for sufficiently large problems many known algorithms are optimal. The central result of the paper is the following sharper lower bound for permutation algorithms. Any permutation algorithm for N data items on a P processor parallel machine without shared memory requires time on the order of N log//kP/P, where K is the maximum number of processors directly connected to a single processor. In particular, a speedup on the order of P is impossible if K is bounded.

Original language | English (US) |
---|---|

Pages (from-to) | 193-209 |

Number of pages | 17 |

Journal | Journal of the ACM |

Volume | 31 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1984 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Graphics and Computer-Aided Design
- Hardware and Architecture
- Information Systems
- Software
- Theoretical Computer Science

### Cite this

*Journal of the ACM*,

*31*(2), 193-209. https://doi.org/10.1145/62.322423

**COMPLEXITY RESULTS FOR PERMUTING DATA AND OTHER COMPUTATIONS ON PARALLEL PROCESSORS.** / Gottlieb, Allan; Kruskal, Clyde P.

Research output: Contribution to journal › Article

*Journal of the ACM*, vol. 31, no. 2, pp. 193-209. https://doi.org/10.1145/62.322423

}

TY - JOUR

T1 - COMPLEXITY RESULTS FOR PERMUTING DATA AND OTHER COMPUTATIONS ON PARALLEL PROCESSORS.

AU - Gottlieb, Allan

AU - Kruskal, Clyde P.

PY - 1984/4

Y1 - 1984/4

N2 - For a wide class of problems, we obtain lower bounds for algorithms executed on certain parallel processors. These bounds show that for sufficiently large problems many known algorithms are optimal. The central result of the paper is the following sharper lower bound for permutation algorithms. Any permutation algorithm for N data items on a P processor parallel machine without shared memory requires time on the order of N log//kP/P, where K is the maximum number of processors directly connected to a single processor. In particular, a speedup on the order of P is impossible if K is bounded.

AB - For a wide class of problems, we obtain lower bounds for algorithms executed on certain parallel processors. These bounds show that for sufficiently large problems many known algorithms are optimal. The central result of the paper is the following sharper lower bound for permutation algorithms. Any permutation algorithm for N data items on a P processor parallel machine without shared memory requires time on the order of N log//kP/P, where K is the maximum number of processors directly connected to a single processor. In particular, a speedup on the order of P is impossible if K is bounded.

UR - http://www.scopus.com/inward/record.url?scp=0021415564&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021415564&partnerID=8YFLogxK

U2 - 10.1145/62.322423

DO - 10.1145/62.322423

M3 - Article

VL - 31

SP - 193

EP - 209

JO - Journal of the ACM

JF - Journal of the ACM

SN - 0004-5411

IS - 2

ER -