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The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement
, 2008
"... To cope with the impossibility of solving agreement problems in asynchronous systems made up of n processes and prone to t process crashes, system designers tailor their algorithms to run fast in “normal” circumstances. Two orthogonal notions of “normality” have been studied in the past through fa ..."
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Cited by 8 (5 self)
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To cope with the impossibility of solving agreement problems in asynchronous systems made up of n processes and prone to t process crashes, system designers tailor their algorithms to run fast in “normal” circumstances. Two orthogonal notions of “normality” have been studied in the past through failure detectors that give processes information about process crashes, and through conditions that restrict the inputs to an agreement problem. This paper investigates how the two approaches can benefit from each other to solve the kset agreement problem, where processes must agree on at most k of their input values (when k = 1 we have the famous consensus problem). It proposes novel failure detectors for solving kset agreement, and a protocol that combines them with conditions, establishing a new bridge among asynchronous, synchronous and partially synchronous systems with respect to agreement problems. The
Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement
"... Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. ..."
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Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. The complexity of set agreement in synchronous networks has also been a significant research challenge. Real systems, however, are neither purely synchronous nor purely asynchronous. Rather, they tend to alternate between periods of synchrony and periods of asynchrony. In this paper, we analyze the complexity of set agreement in a such a “partially synchronous ” setting, presenting the first (asymptotically) tight bound on the complexity of set agreement in such systems. We introduce a novel technique for simulating, in faultprone asynchronous shared memory, executions of an asynchronous and failureprone messagepassing system in which some fragments appear synchronous to some processes. We use this technique to derive a lower bound on the round complexity of set agreement in a partially synchronous system by a reduction from asynchronous waitfree set agreement. We also present an asymptotically matching algorithm that relies on a distributed asynchrony detection mechanism to decide as soon as possible during periods of synchrony. By relating environments with differing degrees of synchrony, our simulation technique is of independent interest. In particular, it allows us to obtain a new lower bound on the complexity of early deciding kset agreement complementary to that of [12], and to rederive the combinatorial topology lower bound of [13] in an algorithmic way. 1
A Topological Treatment of EarlyDeciding SetAgreement
, 2008
"... The ksetagreement problem consists for a set of n processes to agree on less than k among n possibly different values, each initially known to only one process. The problem is at the heart of distributed computing and generalizes the celebrated consensus problem. This paper considers the ksetagr ..."
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The ksetagreement problem consists for a set of n processes to agree on less than k among n possibly different values, each initially known to only one process. The problem is at the heart of distributed computing and generalizes the celebrated consensus problem. This paper considers the ksetagreement problem in a synchronous message passing distributed system where up to t processes can fail by crashing. We determine the number of communication rounds needed for all correct processes to reach a decision in a given run, as a function of the degree of coordination k and the number of processes that actually fail in the run, f ≤ t. We prove that, for any integer 1 ≤ k < n, for any setagreement protocol, for any integer 0 ≤ f ≤ t, not all correct processes can decide within ⌊f/k ⌋ + 1 rounds, in any run with at most f process crashes. More specifically, we prove a lower bound of min(⌊f/k ⌋ + 2, ⌊t/k ⌋ + 1) rounds for earlydeciding setagreement. This bound is tight because there is a setagreement protocol that matches it, and the bound generalizes both the min(f + 2, t + 1) bound previously obtained for earlydeciding consensus and the t + 1 bound previously obtained for the worstcase complexity of setagreement.
Abstract GETCO 2004 Preliminary Version The Complexity of Early Deciding Set Agreement: How can Topology help?
"... The aim of this paper is to pose a challenge to the experts of (algebraic) topology techniques. We present an early deciding algorithm that solves the set agreement problem, i.e., the problem which triggered research on applying topology techniques to distributed computing. We conjecture the algorit ..."
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The aim of this paper is to pose a challenge to the experts of (algebraic) topology techniques. We present an early deciding algorithm that solves the set agreement problem, i.e., the problem which triggered research on applying topology techniques to distributed computing. We conjecture the algorithm to be optimal, and we discuss the need and challenges of applying topology techniques to prove the lower bound.