# Distributed Computation of the Mode

This paper studies the problem of computing the most frequent element (the mode) by means of a distributed algorithm where the elements are located at the nodes of a network. Let k denote the number of distinct elements and further let mi be the number of occurrences of the element ei in the ordered list of occurrences m1 > m2 ≥ ... ≥ mk. We give a deterministic distributed algorithm with time complexity O(D+k) where D denotes the diameter of the graph, which is essentially tight. As our main contribution, a Monte Carlo algorithm is presented which computes the mode in O(D + F2/m2 1 · log k) time with high probability, where the frequency moment F` is de�ned as F` = Pk i=1 m` i . This algorithm is substantially faster than the deterministic algorithm for various relevant frequency distributions. Moreover, we provide a lower bound of Ω(D +F5/(m5 1B)), where B is the maximum message size, that captures the e�ect of the frequency distribution on the time complexity to compute the mode.

Top- Locher, Thomas
- Kuhn, Fabian
- Schmid, Stefan

Category |
Paper in Conference Proceedings or in Workshop Proceedings (Paper) |

Event Title |
27th Annual ACM Symposium on Principles of Distributed Computing (PODC) |

Divisions |
Communication Technologies |

Subjects |
Informatik Allgemeines |

Event Location |
Toronto, Canada |

Event Type |
Conference |

Event Dates |
August 2008 |

Date |
2008 |

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