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 to be of the 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 another 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 [17] 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.