## Abstract

In this paper we introduce a new network model called a multimedia network. It combines the point-to-point message passing network and the multiaccess channel. To benefit from the combination we design algorithms which consist of two stages: a local stage which utilizes the parallelism of the point-to-point network and a global stage which utilizes the broadcast capability of the multiaccess channel. As a reasonable approach, one wishes to balance the complexities of the two stages by obtaining an efficient partition of the network into O(√n) connected components each of radius O(√n). To this end we present efficient deterministic and randomized partitioning algorithms. The deterministic algorithm runs in O(√n log^{∗} n) time and O(m + n log n log^{∗} n) messages, where n and m are the number of nodes and number of point-to-point links in the network. The randomized algorithm runs in the same time, but sends only O(m+ n log^{∗} n) messages. The partitioning algorithms are then used to obtain: (1) O(√n log n log^{∗} n) time deterministic and O(√n log^{∗} n) time randomized algorithms for computing global sensitive functions, and (2) O(√n log n) time deterministic algorithm for computing a minimum spanning tree. An Ω(n) time lower bounds for computing global sensitive functions in both point-topoint and multiaccess networks, are given, thus showing that the multimedia network is more powerful than both its separate components. Furthermore, we prove an Ω(√n) time lower bound for multimedia networks, thus leaving a small gap between our upper and lower bounds.

Original language | English |
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Title of host publication | Proceedings of the 7th Annual ACM Symposium on Principles of Distributed Computing, PODC 1988 |

Publisher | Association for Computing Machinery |

Pages | 90-104 |

Number of pages | 15 |

ISBN (Electronic) | 0897912772 |

DOIs | |

State | Published - 1 Jan 1988 |

Externally published | Yes |

Event | 7th Annual ACM Symposium on Principles of Distributed Computing, PODC 1988 - Toronto, Canada Duration: 15 Aug 1988 → 17 Aug 1988 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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Volume | Part F130192 |

### Conference

Conference | 7th Annual ACM Symposium on Principles of Distributed Computing, PODC 1988 |
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Country/Territory | Canada |

City | Toronto |

Period | 15/08/88 → 17/08/88 |

### Funding

Funders | Funder number |
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Applied Mathematical Sciences | |

IBM Research Division | |

U.S. Department of Energy | DE-AC02 76ERO3077 |

Office of Energy Research and Development |