NDLI: Distributed computation of the mode

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Distributed computation of the mode

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Distributed computation of the mode

Content Provider	ACM Digital Library
Author	Schmid, Stefan Locher, Thomas Kuhn, Fabian
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 $m_{i}$ be the number of occurrences of the element $e_{i}$ in the ordered list of occurrences $m_{1}m_{2}≥$ . ≥ $m_{k}.$ 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 + $F_{2}/m_{1}^{2}*log$ k) time with high probability, where the frequency moment $F_{t}$ is defined as $F_{t}$ = $sum_{i=1}^{k}$ $m_{i}^{t}.$ This algorithm is substantially faster than the deterministic algorithm for various relevant frequency distributions. Moreover, we provide a lower bound of $Omega(D+F_{5}/(m_{1}^{5}B)),$ where B is the maximum message size, that captures the effect of the frequency distribution on the time complexity to compute the mode.
Starting Page	15
Ending Page	24
Page Count	10
File Format	PDF
ISBN	9781595939890
DOI	10.1145/1400751.1400756
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-08-18
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Aggregation Mode Most frequent element Distributed algorithms
Content Type	Text
Resource Type	Article

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