Optimal adaptive broadcasting with a bounded fraction of faulty nodes

Abstract

We consider broadcasting among n processors, f of which can be faulty. A fault-free processor, called the source, holds a piece of information which has to be transmitted to all other fault-free processors. We assume that the fraction f /n of faulty processors is bounded by a constant ,γ < 1. Transmissions are fault free. Faults are assumed of crash, type: faulty processors do not send or receive messages. We use the whispering model: pairs of processors communicating in one round must form a matching. A fault-free processor sending a message to an other processor becomes aware of whether this processor is faulty or fault free and can adapt future transmissions accordingly. The main result of the paper is a broadcasting algorithm working in O(log n) rounds and using O(n) messages of logarithmic size, in the worst case. This is an improvement of the result from [10] where O((log n)2) rounds were used. Our method also gives the first algorithm for adaptive distributed fault diagnosis in O (log n) rounds.