## Abstract

In this paper we develop a leader election protocol P with the following features: The protocol runs in the perfect information model: Every step taken by a player is visible to all others. It has linear immunity: If P is run by n players and a coalition of c1n players deviates from the protocol, attempting to have one of them elected, their probability of success is < 1 -C2, where Ci, c2 > 0 are absolute constants. It is fast : The running time of P is poly- logarithmic in n, the number of players. A previous protocol by Alon and Naor achieving linear immunity in the perfect information model has a linear time complexity. The main ingredient of our protocol is a reduction subpro-Tocol. This is a way for n players to elect a subset of themselves which has the following property. Assume that up to €n of the players are bad and try to have as many of them elected to the subset. Then with high probability, the fraction of bad players among the elected ones will not exceed € in a significant way. The existence of such a reduction protocol is first established by a probabilistic argument. Later an explicit construction is provided which is based on the spectral properties of Ramanujan graphs.

Original language | American English |
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Title of host publication | Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993 |

Publisher | Association for Computing Machinery |

Pages | 662-671 |

Number of pages | 10 |

ISBN (Electronic) | 0897915917 |

DOIs | |

State | Published - 1 Jun 1993 |

Event | 25th Annual ACM Symposium on Theory of Computing, STOC 1993 - San Diego, United States Duration: 16 May 1993 → 18 May 1993 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F129585 |

ISSN (Print) | 0737-8017 |

### Conference

Conference | 25th Annual ACM Symposium on Theory of Computing, STOC 1993 |
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Country/Territory | United States |

City | San Diego |

Period | 16/05/93 → 18/05/93 |

### Bibliographical note

Funding Information:* Hebrew University, Jerusalem. Work supported part by grants from the Binational Science Foundation Israel-US and from the Israeli Academy of Sciences. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its data appear, and notice is given that copying is by permission of the Association for Computing Machinary. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,LJSA 01993 ACM 0-89791 -591 -71931000510662

Publisher Copyright:

© 1993 ACM.