NDLI: Tight bounds for k-set agreement with limited-scope failure detectors

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Tight bounds for k-set agreement with limited-scope failure detectors

Content Provider	Springer Nature Link
Author	Herlihy, M. Penso, L. D.
Copyright Year	2005
Abstract	In a system with limited-scope failure detectors, there are q disjoint clusters of processes such that some correct process in each cluster is never suspected by any process in that cluster. The failure detector class Sx,q satisfies this property all the time, while ⋄Sx,q satisfies it eventually. This paper gives the first tight bounds for the k-set agreement task in asynchronous message-passing models augmented with failure detectors from either the Sx,q or ⋄Sx,q classes. For Sx,q, we show that any k-set agreement protocol that tolerates f failures must satisfy f < k + x − q if q < k and f < x otherwise, where x is the combined size of the q disjoint clusters if q < k (or the k largest, otherwise). This result establishes for the first time that the protocol of Mostèfaoui and Raynal for the Sx = Sx,1 failure detector is optimal.For ⋄Sx,q, we show that any k-set agreement protocol that tolerates f failures must satisfy $$ f \textless \hbox{min}(\frac{n+1}{2},k+x-q) $$ if q < k and $$ f \textless \hbox{min}(\frac{n+1}{2},x) $$ otherwise, where n + 1 is the total number of processes. We give a novel protocol that matches our lower bound, disproving a conjecture of Mostèfaoui and Raynal for the ⋄Sx = ⋄Sx,1 failure detector.Our lower bounds exploit techniques borrowed from Combinatorial Topology, demonstrating for the first time that this approach is applicable to models that encompass failure detectors.
Starting Page	157
Ending Page	166
Page Count	10
File Format	PDF
ISSN	01782770
Journal	Distributed Computing
Volume Number	18
Issue Number	2
e-ISSN	14320452
Language	English
Publisher	Springer-Verlag
Publisher Date	2005-09-23
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computer Hardware Computer Systems Organization and Communication Networks Software Engineering/Programming and Operating Systems Theory of Computation Computer Communication Networks
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computer Networks and Communications Computational Theory and Mathematics Hardware and Architecture

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