### Abstract

We show improved bounds for 1-1 routing and sorting on multi-dimensional meshes and tori. In particular, we give a fairly simple deterministic algorithm for sorting on the (/-dimensional mesh of side length n that achieves a running time of 3dn/2+o(n) without making any copies of the elements. We give deterministic algorithms with running times of 5dn/4 + o(n) and Zdn/4 + o(n) for the d-dimensional mesh and torus, respectively, that make one copy of each element. We also show lower bounds for sorting with respect to a large class of indexing schemes, under a model of the mesh where each processor can hold an arbitrary number of packets. Finally, we describe algorithms for permutation routing whose running times come very close to the diameter lower bound.

Original language | English (US) |
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Title of host publication | Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994 |

Publisher | Association for Computing Machinery, Inc |

Pages | 26-35 |

Number of pages | 10 |

ISBN (Electronic) | 0897916719, 9780897916714 |

DOIs | |

State | Published - Aug 1 1994 |

Event | 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994 - Cape May, United States Duration: Jun 27 1994 → Jun 29 1994 |

### Other

Other | 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994 |
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Country | United States |

City | Cape May |

Period | 6/27/94 → 6/29/94 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture

### Cite this

*Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994*(pp. 26-35). Association for Computing Machinery, Inc. https://doi.org/10.1145/181014.181022

**Improved bounds for routing and sorting on multi-dimensional meshes.** / Suel, Torsten.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994.*Association for Computing Machinery, Inc, pp. 26-35, 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994, Cape May, United States, 6/27/94. https://doi.org/10.1145/181014.181022

}

TY - GEN

T1 - Improved bounds for routing and sorting on multi-dimensional meshes

AU - Suel, Torsten

PY - 1994/8/1

Y1 - 1994/8/1

N2 - We show improved bounds for 1-1 routing and sorting on multi-dimensional meshes and tori. In particular, we give a fairly simple deterministic algorithm for sorting on the (/-dimensional mesh of side length n that achieves a running time of 3dn/2+o(n) without making any copies of the elements. We give deterministic algorithms with running times of 5dn/4 + o(n) and Zdn/4 + o(n) for the d-dimensional mesh and torus, respectively, that make one copy of each element. We also show lower bounds for sorting with respect to a large class of indexing schemes, under a model of the mesh where each processor can hold an arbitrary number of packets. Finally, we describe algorithms for permutation routing whose running times come very close to the diameter lower bound.

AB - We show improved bounds for 1-1 routing and sorting on multi-dimensional meshes and tori. In particular, we give a fairly simple deterministic algorithm for sorting on the (/-dimensional mesh of side length n that achieves a running time of 3dn/2+o(n) without making any copies of the elements. We give deterministic algorithms with running times of 5dn/4 + o(n) and Zdn/4 + o(n) for the d-dimensional mesh and torus, respectively, that make one copy of each element. We also show lower bounds for sorting with respect to a large class of indexing schemes, under a model of the mesh where each processor can hold an arbitrary number of packets. Finally, we describe algorithms for permutation routing whose running times come very close to the diameter lower bound.

UR - http://www.scopus.com/inward/record.url?scp=0039755757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039755757&partnerID=8YFLogxK

U2 - 10.1145/181014.181022

DO - 10.1145/181014.181022

M3 - Conference contribution

SP - 26

EP - 35

BT - Proceedings of the 6th Annual ACM Symposium on Parallel Algorithms and Architectures, SPAA 1994

PB - Association for Computing Machinery, Inc

ER -