From a static impossibility to an adaptive lower bound: the complexity of early deciding set agreement

Set agreement, where processors decisions constitute a set of outputs, is notoriously harder to analyze than consensus where the decisions are restricted to a single output. This is because the topological questions that underly set agreement are not about simple connectivity as in consensus. Analyzing set agreement inspired the discovery of the relation between topology and distributed algorithms, and consequently the impossibility of set agreement. Yet, the application of topological reasoning has been to the static case, that of asynchronous and synchronous tasks. It is not known yet for example, how to characterize starvation-free solvability of non-terminating tasks. Non-terminating tasks are dynamic entities with no defined end. In a similar vain, early deciding synchronous set agreement, in which the number of rounds it takes a processor to decide adapts to the actual number of failures, falls in this category of dynamic entities. This paper develops a simulation technique that...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Eli Gafni, Rachid Guerraoui, Bastian Pochon
• Keywords: Algorithms, Set Agreement, STOC 2005, Synchronous Set Agreement, Underly Set Agreement