Solving k-Set Agreement with Stable Skeleton Graphs

TL;DR

This paper introduces a new approach to solve the k-set agreement problem in distributed systems by using stable skeleton graphs and a novel communication predicate, providing tight bounds and an effective algorithm.

Contribution

It defines the weak communication predicate PSources(k), proves its tightness for k-set agreement, and presents a distributed algorithm based on local approximations of the stable skeleton graph.

Findings

PSources(k) is tight for k-set agreement.

The proposed algorithm achieves k-set agreement under PSources(k).

Stable skeleton graph approximations are correct and useful for solving k-set agreement.

Abstract

In this paper we consider the k-set agreement problem in distributed message-passing systems using a round-based approach: Both synchrony of communication and failures are captured just by means of the messages that arrive within a round, resulting in round-by-round communication graphs that can be characterized by simple communication predicates. We introduce the weak communication predicate PSources(k) and show that it is tight for k-set agreement, in the following sense: We (i) prove that there is no algorithm for solving (k-1)-set agreement in systems characterized by PSources(k), and (ii) present a novel distributed algorithm that achieves k-set agreement in runs where PSources(k) holds. Our algorithm uses local approximations of the stable skeleton graph, which reflects the underlying perpetual synchrony of a run. We prove that this approximation is correct in all runs, regardless of the communication predicate, and show that graph-theoretic properties of the stable skeleton graph can be used to solve k-set agreement if PSources(k) holds.