### Abstract

The authors prove a lower bound of Omega (log n/log log n) on the competitive ratio of any (deterministic or randomised) distributed algorithm for solving the mobile user problem on certain networks of n processors. The lower bound holds for various networks, including the hypercube, any network with sufficiently large girth, and any highly expanding graph. A similar Omega (log n/log log n) lower bound is proved for the competitive ratio of the maximum job delay of any distributed algorithm for solving a distributed scheduling problem on any of these networks. The proofs combine combinatorial techniques with tools from linear algebra and harmonic analysis and apply, in particular, a generalization of the vertex isoperimetric problem on the hypercube, which may be of independent interest.

Original language | English (US) |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 334-343 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: Oct 24 1992 → Oct 27 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country | United States |

City | Pittsburgh |

Period | 10/24/92 → 10/27/92 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)

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## Cite this

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992*(pp. 334-343). [267757] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October). IEEE Computer Society. https://doi.org/10.1109/SFCS.1992.267757