Guessing Games and Distributed Computations in Synchronous Networks

1. INTRODUCTION 1.1 Background and Motivations A distributed system is a network G=(V,E) of |V|=n processors connected by |E|=e direct communication links, where each processor has a local non-shared memory and can communicate by sending messages to and receiving messages from its neighbours. The behaviour of these processors can be conveniently described as finite-state and event-driven; that is, each processor at any time is in a particular state and, when a predefined event occurs (e.g., a message is received, the internal clock reaches a predetermined value, etc.), it will serially perform some operations whose nature depends on the current state and on the occurred event. The operations that can be performed are local computations, transmission of messages, and change of state. A distributed algorithm is the specification of what operations must be serially performed by a processor when a predefined event occurs in a given state. To ensure a fully distributed computation in the system, it is assumed that every processor has the same algorithm. A fundamental computation in this environment is the election process; that is, the process of changing from an initial system configuration, where every processor in the network is in the same state, to a final configuration where exactly one processor is in a predefined state (say, elected) and all other processors are in another predefined state (say, defeated). Note that there is no a-priori restriction on which processor should become elected.