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Distributed computation of the mode

Published: 18 August 2008 Publication History

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 m1m2≥ ... ≥ 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/m12*log k) time with high probability, where the frequency moment Ft is defined as Ft = sumi=1k mit. This algorithm is substantially faster than the deterministic algorithm for various relevant frequency distributions. Moreover, we provide a lower bound of Omega(D+F5/(m15B)), where B is the maximum message size, that captures the effect of the frequency distribution on the time complexity to compute the mode.

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  • (2015)Distributed Outlier Detection using Compressive SensingProceedings of the 2015 ACM SIGMOD International Conference on Management of Data10.1145/2723372.2747641(3-16)Online publication date: 27-May-2015
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cover image ACM Conferences
PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
August 2008
474 pages
ISBN:9781595939890
DOI:10.1145/1400751
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 18 August 2008

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Author Tags

  1. aggregation
  2. distributed algorithms
  3. mode
  4. most frequent element

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Cited By

View all
  • (2021)Efficient distributed algorithms for holistic aggregation functions on random regular graphsScience China Information Sciences10.1007/s11432-020-2996-265:5Online publication date: 27-May-2021
  • (2015)Distributed Graph Algorithms and their Complexity: An IntroductionInterdisciplinary Information Sciences10.4036/iis.2015.L.0421:4(351-370)Online publication date: 2015
  • (2015)Distributed Outlier Detection using Compressive SensingProceedings of the 2015 ACM SIGMOD International Conference on Management of Data10.1145/2723372.2747641(3-16)Online publication date: 27-May-2015
  • (2015)Revisiting Democratic Mining in BitcoinsProceedings of the 11th International Conference on Information Systems Security - Volume 947810.1007/978-3-319-26961-0_10(161-170)Online publication date: 16-Dec-2015
  • (2015)Proceedings of the 2015 ACM SIGMOD International Conference on Management of DataundefinedOnline publication date: 27-May-2015
  • (2014)Continuous Aggregation in Dynamic Ad-Hoc NetworksStructural Information and Communication Complexity10.1007/978-3-319-09620-9_16(194-209)Online publication date: 2014
  • (2012)Tracking distributed aggregates over time-based sliding windowsProceedings of the 24th international conference on Scientific and Statistical Database Management10.1007/978-3-642-31235-9_28(416-430)Online publication date: 25-Jun-2012
  • (2011)The complexity of data aggregation in directed networksProceedings of the 25th international conference on Distributed computing10.5555/2075029.2075082(416-431)Online publication date: 20-Sep-2011
  • (2011)Tracking distributed aggregates over time-based sliding windowsProceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing10.1145/1993806.1993839(213-214)Online publication date: 6-Jun-2011
  • (2011)The Complexity of Data Aggregation in Directed NetworksDistributed Computing10.1007/978-3-642-24100-0_40(416-431)Online publication date: 2011

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