Making Local Algorithms Wait-Free: the Case of Ring Coloring

When considering distributed computing, reliable message-passing synchronous systems on the one side, and asynchronous failure-prone shared-memory systems on the other side, remain two quite independently studied ends of the reliability/asynchrony spectrum. The concept of locality of a computation is central to the first one, while the concept of wait-freedom is central to the second one. The paper proposes a new DECOUPLED model in an attempt to reconcile these two worlds. It consists of a synchronous and reliable communication graph of n nodes, and on top a set of asynchronous crash-prone processes, each attached to a communication node. To illustrate the DECOUPLED model, the paper presents an asynchronous 3-coloring algorithm for the processes of a ring. From the processes point of view, the algorithm is wait-free. From a locality point of view, each process uses information only from processes at distance O(log ^* n) from it. This local wait-free algorithm is based on an extension of the classical Cole and Vishkin’s vertex coloring algorithm in which the processes are not required to start simultaneously.