Distributed Computation of the Mode

Distributed Computation of the Mode

Abstract

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.

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Authors
  • Locher, Thomas
  • Kuhn, Fabian
  • Schmid, Stefan
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Supplemental Material
Shortfacts
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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