In this exercise we consider the problem of $[k, l]$-election, which generalizes the usual election problem. The problem requires that all correct processes decide on either 0 ("defeated") or $s 11$ ("elected"), and that the number of processes that decide 1 is between $k$ and $l$ (inclusive). (1) What are the uses of $[k, l]$-election? (2) Demonstrate that no deterministic 1-crash robust algorithm for $[k, k]$ election exists.(if $0<k<N$ ). (3) Give a deterministic $t$-crash robust algorithm for $[k, k+2 t]$-election.

    In this exercise we consider the problem of $[k, l]$-election, which generalizes the usual election problem. The problem requires that all correct processes decide on either 0 ("defeated") or $s 11$ ("elected"), and that the number of processes that decide 1 is between $k$ and $l$ (inclusive).
(1) What are the uses of $[k, l]$-election?
(2) Demonstrate that no deterministic 1-crash robust algorithm for $[k, k]$ election exists.(if $0<k<N$ ).
(3) Give a deterministic $t$-crash robust algorithm for $[k, k+2 t]$-election.

Introduction to Distributed Algorithms

Gerard Tel 1st Edition

Chapter 13, Problem 8

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However, some potential uses could include: - Decision-making processes where a certain number of votes or approvals are required for an action to be taken. For example, in a committee or board, a decision may require at least $k$ votes in favor and no more than Show more…

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In this exercise we consider the problem of $[k, l]$-election, which generalizes the usual election problem. The problem requires that all correct processes decide on either 0 ("defeated") or $s 11$ ("elected"), and that the number of processes that decide 1 is between $k$ and $l$ (inclusive). (1) What are the uses of $[k, l]$-election? (2) Demonstrate that no deterministic 1-crash robust algorithm for $[k, k]$ election exists.(if $0<k<N$ ). (3) Give a deterministic $t$-crash robust algorithm for $[k, k+2 t]$-election.

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