TY - GEN

T1 - Dependable decentralized cooperation with the help of reliability estimation

AU - Davtyan, Seda

AU - Konwar, Kishori M.

AU - Shvartsman, Alexander A.

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2014

Y1 - 2014

N2 - Internet supercomputing aims to solve large partitionable computational problems by using vast numbers of computers. Here we consider the abstract version of the problem, where n processors perform t independent tasks, with n ≤ t, and each processor learns the results of all tasks. An adversary may cause a processor to return incorrect results, and to crash. Prior solutions limited the adversary by either (i) assuming the average probability of returning incorrect results to always be inferior to 1/2, or (ii) letting each processor know such probabilities for all other processors. This paper presents a new randomized synchronous algorithm that deals with stronger adversaries while achieving efficiency comparable to the weaker solutions. The adversary is constrained in two ways. (1) The set of non-crashed processors must contain a hardened subset H of the initial set of processors P, for which the average probability of returning a bogus result is inferior to 1/2. Notably, crashes may increase the average probability of processor misbehavior. (2) The adversary may crash a set of processors F, provided |P−F| is bounded from below. We analyse the algorithm for three bounds on |P−F|: (a) when the bound is linear in n the algorithm takes Θ(t/n log n) communication rounds, has work complexity Θ(t log n), and message complexity O(n log2 n); (b) when the bound is polynomial (|P−F| = Ω(na), for a constant a ∈ (0, 1)), the algorithm takes O(t/na log n log log n) rounds, with work O(t log n log log n), and message complexity O(n log2 n log log n); (c) when the bound is polylog in n, it takes O(t) rounds, has work O(t·na), and message complexity O(n1+a), for a ∈ (0, 1).

AB - Internet supercomputing aims to solve large partitionable computational problems by using vast numbers of computers. Here we consider the abstract version of the problem, where n processors perform t independent tasks, with n ≤ t, and each processor learns the results of all tasks. An adversary may cause a processor to return incorrect results, and to crash. Prior solutions limited the adversary by either (i) assuming the average probability of returning incorrect results to always be inferior to 1/2, or (ii) letting each processor know such probabilities for all other processors. This paper presents a new randomized synchronous algorithm that deals with stronger adversaries while achieving efficiency comparable to the weaker solutions. The adversary is constrained in two ways. (1) The set of non-crashed processors must contain a hardened subset H of the initial set of processors P, for which the average probability of returning a bogus result is inferior to 1/2. Notably, crashes may increase the average probability of processor misbehavior. (2) The adversary may crash a set of processors F, provided |P−F| is bounded from below. We analyse the algorithm for three bounds on |P−F|: (a) when the bound is linear in n the algorithm takes Θ(t/n log n) communication rounds, has work complexity Θ(t log n), and message complexity O(n log2 n); (b) when the bound is polynomial (|P−F| = Ω(na), for a constant a ∈ (0, 1)), the algorithm takes O(t/na log n log log n) rounds, with work O(t log n log log n), and message complexity O(n log2 n log log n); (c) when the bound is polylog in n, it takes O(t) rounds, has work O(t·na), and message complexity O(n1+a), for a ∈ (0, 1).

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UR - http://www.scopus.com/inward/citedby.url?scp=84908266340&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-11764-5_20

DO - 10.1007/978-3-319-11764-5_20

M3 - Conference contribution

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 283

EP - 298

BT - Stabilization, Safety and Security of Distributed Systems

A2 - Felber, Pascal

A2 - Garg, Vijay K.

PB - Springer Verlag

ER -