### Abstract

We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete networkK_{n} of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any configuration of up to f layouts and have a least possible congestion. First, we study the minimal congestion of 1- hop f-tolerant layouts in K_{n}. For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network K_{n}[F] which results from K_{n} by deleting links from a set F of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in K_{n}, for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution. Links fail independently with constant probability p < 1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p < 1, we show such layouts in K_{n}, with congestion O(log n).

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 1996 - 21st International Symposium, MFCS 1996, Proceedings |

Editors | Andrzej Szalas, Wojciech Penczek |

Publisher | Springer Verlag |

Pages | 372-381 |

Number of pages | 10 |

ISBN (Print) | 3540615504, 9783540615507 |

State | Published - Jan 1 1996 |

Externally published | Yes |

Event | 21st International Symposium on Mathematical Foundations of Computer Science, MFCS 1996 - Cracow, Poland Duration: Sep 2 1996 → Sep 6 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1113 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 21st International Symposium on Mathematical Foundations of Computer Science, MFCS 1996 |
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Country | Poland |

City | Cracow |

Period | 9/2/96 → 9/6/96 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Mathematical Foundations of Computer Science 1996 - 21st International Symposium, MFCS 1996, Proceedings*(pp. 372-381). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1113). Springer Verlag.