Alistarh, Dan-AdrianISTA; Gilbert, Seth; Guerraoui, Rachid; Travers, Corentin
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 fault-tolerant 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 "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 fault-prone asynchronous shared memory, executions of an asynchronous and failure-prone 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 wait-free 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 k-set agreement complementary to that of , and to re-derive the combinatorial topology lower bound of  in an algorithmic way.
Corentin Travers was supposrted in part by a Sam & Cecilia Neaman Fellowship
943 - 953
ISAAC: International Symposium on Algorithms and Computation
Alistarh D-A, Gilbert S, Guerraoui R, Travers C. Of choices, failures and asynchrony: the many faces of set agreement. In: Vol 5878 LNCS. Springer; 2009:943-953. doi:10.1007/978-3-642-10631-6_95
Alistarh, D.-A., Gilbert, S., Guerraoui, R., & Travers, C. (2009). Of choices, failures and asynchrony: the many faces of set agreement (Vol. 5878 LNCS, pp. 943–953). Presented at the ISAAC: International Symposium on Algorithms and Computation, Springer. https://doi.org/10.1007/978-3-642-10631-6_95
Alistarh, Dan-Adrian, Seth Gilbert, Rachid Guerraoui, and Corentin Travers. “Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement,” 5878 LNCS:943–53. Springer, 2009. https://doi.org/10.1007/978-3-642-10631-6_95.
D.-A. Alistarh, S. Gilbert, R. Guerraoui, and C. Travers, “Of choices, failures and asynchrony: the many faces of set agreement,” presented at the ISAAC: International Symposium on Algorithms and Computation, 2009, vol. 5878 LNCS, pp. 943–953.
Alistarh D-A, Gilbert S, Guerraoui R, Travers C. 2009. Of choices, failures and asynchrony: the many faces of set agreement. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 5878 LNCS, 943–953.
Alistarh, Dan-Adrian, et al. Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement. Vol. 5878 LNCS, Springer, 2009, pp. 943–53, doi:10.1007/978-3-642-10631-6_95.