Minimum time broadcast in faulty star networks

In this paper we give new results on the fault{tolerance capabilities of the star graph. We rst consider the problem of determining the maximum number r(n) of vertices in a n! vertices star graph S n such that by removing any set of vertices and/or edges from S n of cardinality at most r(n) the diameter of S n does not increase. Subsequently, we give an algorithm for broadcasting a message in S n in optimal time (the diameter of S n) and using the minimum possible number of message transmissions, i.e., n! ? 1, in presence of up to r(n) vertex or edge faults, assuming the set of faults is known to all vertices of the network. We also extend this result to the case in which there is no global knowledge on the faulty elements.