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Chapter 2 Consensus & Classic Paxos We begin our study of distributed consensus by first considering how to decide upon a single value between a set of participants. This task, whilst seemingly simple, will occupy us for the majority of this thesis. Single-valued agreement is often overlooked in the literature as already solved or trivial and is seldom considered at length, despite being a vital component in distributed systems which is infamously poorly understood. This chapter is broadly divided into three parts. We begin by defining the requirements for an algorithm to solve distributed consensus (§2.1). Secondly, we outline two existing algorithms which solve single valued consensus: the single acceptor algorithm (§2.1.1), a na ̈ıve straw man solution and Classic Paxos (§2.2, §2.3, §2.4), the widely adopted solution which lies at the foundation of a broad range of complex distributed systems. Thirdly and finally, we go on to prove that both algorithms satisfy all of the requirements of distributed consensus as defined in the first part (§2.5,2.6,2.7). 2.1 Preliminaries Single valued distributed consensus is the problem of deciding a single value v ∈ V between a finite set of n participants, U = {u1,u2,...,un}. Definition 1. An algorithm is said to solve distributed consensus only if it satisfies the following three safety requirements: Non-triviality The decided value must have been proposed by a participant. Safety If a value has been decided, no other value will be decided. Safe learning If a participant learns a value, it must learn the decided value. 21PDF Image | Distributed consensus
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