eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
42:1
42:13
10.4230/LIPIcs.ISAAC.2020.42
article
Multiparty Selection
Chen, Ke
1
https://orcid.org/0000-0001-5470-6621
Dumitrescu, Adrian
1
https://orcid.org/0000-0002-1118-0321
Department of Computer Science, University of Wisconsin-Milwaukee, WI, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.42/LIPIcs.ISAAC.2020.42.pdf
approximate selection
mediocre element
comparison algorithm
i-th order statistic
tournaments
quantiles
communication complexity