## Abstract

We consider a broad class of communication tasks, which we call isotropic, in a hypercube and in a wraparound mesh of processors. These tasks are characterized by a type of symmetry with respect to origin node. We show that executing such tasks in a minimum number of steps is equivalent to a matrix decomposition problem. We use this property to obtain minimum completion time algorithms. For a special communication task, the total exchange problem, we find algorithms that are simultaneously optimal with respect to completion time, and average packet delay. We also prove that a particularly simple type of shortest path algorithm executes isotropic tasks in time which is optimal within a small bound.

Original language | English (US) |
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Pages (from-to) | 1233-1257 |

Number of pages | 25 |

Journal | Parallel Computing |

Volume | 18 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1992 |

Externally published | Yes |

## Keywords

- Communication algorithm
- hypercube
- optimal completion time algorithms
- symmetric routing algorithms
- total exchange problem

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computer Graphics and Computer-Aided Design
- Artificial Intelligence