Condition-based consensus solvability: a hierarchy of conditions and efficient protocols

Abstract

The condition-based approach for consensus solvability consists of identifying sets of input vectors, called conditions, for which there exists an asynchronous protocol solving consensus despite the occurrence of up to f process crashes. This paper investigates C f , the largest set of conditions which allow us to solve the consensus problem in an asynchronous shared memory system.The first part of the paper shows that C f is made up of a hierarchy of classes of conditions, CWe prove that each one is strictly contained in the previous one: CVarious properties of the hierarchy are also derived. It is shown that a class can be characterized in two equivalent but complementary ways: one is convenient for designing protocols while the other is for analyzing the class properties. The paper also defines a linear family of conditions that can be used to derive many specific conditions. In particular, for each d, two natural conditions are presented.The second part of the paper is devoted to the design of efficient condition-based protocols. A generic conditionbased protocol is presented. This protocol can be instantiated with any condition C, C ∈ C [d] f , and requires at most (2n+1) log 2 ( (f − d)/2 + 1) shared memory read/write operations per process in the synchronization part of the protocol. Thus, the value (f − d) represents the "difficulty" of the class C [d] f . An improvement of the protocol for the conditions in C[0] f is also presented.

Byzantine consensus in asynchronous message-passing systems: a survey

“…Last but not the least, this section describes how FLP can be circumvented by weakening the very definition of consensus, i.e., by modifying it. Currently, we are aware of a single type of algorithm that fits in this category in the system model that we consider in the paper: algorithms based on the condition-based approach (Mostefaoui et al, 2003b(Mostefaoui et al, , 2004Friedman et al, 2002). For crash faults, there is also k-set consensus, which allows k different values to be decided (Chaudhuri, 1993).…”

The Combined Power of Conditions and Information on Failures to Solve Asynchronous Set Agreement

“…• For values of d ≤ 0, for inputs in C consensus is solvable by more and more efficient protocols in a shared memory asynchronous system as we go from d = 0 to d = −t [40].…”

Constraint-Based Deployment of Distributed Components in a Dynamic Network

“…We use the results of [12], in which the requirements of the consensus problem are relaxed. The authors have identified conditions for which there exists an asynchronous protocol that solves the consensus problem despite the occurrence of t process crashes.…”

“…The only change concerns the designation of a representative host for each node of the hierarchy. We use the algorithm of [12] to elect such a representative and to build a common view of the placement of the components.…”