Fast consensus under eventually stabilizing message adversaries

Abstract

This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of 2D +1 for the termination time of consensus under a message adversary that eventually guarantees a single vertexstable root component with dynamic network diameter D, as well as a simple algorithm that matches this bound. It effectively halves the termination time 4D + 1 achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.

Consensus in rooted dynamic networks with short-lived stability

“…(3) To complement earlier results [22] about consensus algorithms that work for stability periods longer than 2D + 1, we show in Section 6 that very large periods of stability, namely, at least 3n − 3, also allow to adopt the well-known uniform voting algorithm [8] for solving consensus in our setting.…”

“…We now prove the correctness of Algorithm 1 under ♦STABLE D (D + 1). As shown in [21,Lemmas 3 and 4], the simple graph approximation algorithm running underneath our consensus algorithm allows processes to faithfully detect root components under certain circumstances. Denoting process p's round r estimate of root(G s ) as root r p (s), the following two key features can be guaranteed algorithmically (we assume that root r p (s) returns {⊥} if p is unsure about its estimate):…”

“…We also explore the solvability/impossibility border of consensus, albeit under non-oblivious message adversaries that support eventual stabilization [3,4,22]: Here, the set of admissible choices for G r may change with evolving round numbers r. Rather than constraining the set of admissible graphs, we hence constrain admissible graph sequences. As it turns out, consensus can be solved for graph sequences where the set of graphs occurring in the sequence would render consensus impossible under an oblivious message adversary [9,19].…”

“…Thanks to (i), our algorithm is always safe in the sense that agreement is never violated; (ii) is only needed to ensure termination. Compared to all existing algorithms for non-oblivious mes-sage adversaries like [3,4,22], where the processes more or less wait for the stability window to occur, our algorithm uses quite different algorithmic techniques.…”

On Knowledge and Communication Complexity in Distributed Systems

“…In [SWS16], a message adversary has been presented that guarantees rooted graphs and the eventual existence of a single vertex-stable root for 2D + 1 rounds. An algorithm has been provided, which solves consensus under this message adversary.…”