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Multiparty Selection

Authors Ke Chen , Adrian Dumitrescu

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Ke Chen
  • Department of Computer Science, University of Wisconsin-Milwaukee, WI, USA
Adrian Dumitrescu
  • Department of Computer Science, University of Wisconsin-Milwaukee, WI, USA

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Ke Chen and Adrian Dumitrescu. Multiparty Selection. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.42

Abstract

Given a sequence A of n numbers and an integer (target) parameter 1 ≤ i ≤ n, the (exact) selection problem is that of finding the i-th smallest element in A. An element is said to be (i,j)-mediocre if it is neither among the top i nor among the bottom j elements of S. The approximate selection problem is that of finding an (i,j)-mediocre element for some given i,j; as such, this variant allows the algorithm to return any element in a prescribed range. In the first part, we revisit the selection problem in the two-party model introduced by Andrew Yao (1979) and then extend our study of exact selection to the multiparty model. In the second part, we deduce some communication complexity benefits that arise in approximate selection. In particular, we present a deterministic protocol for finding an approximate median among k players.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • approximate selection
  • mediocre element
  • comparison algorithm
  • i-th order statistic
  • tournaments
  • quantiles
  • communication complexity

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