MINIMUM-TIME BROADCAST IN FAULTY STAR NETWORKS

In this paper we give new results on the fault-tolerance capabilities of the star graph. We first consider the problem of determining the ma ximum number r(n) of vertices in a ii! vertices star graph S-n such th at by removing any set of vertices and/or edges from S-n of cardinalit y at most r(n) the diameter of S,, 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 net work. We also extend this result to the case in which there is no glob al knowledge on the faulty elements. (C) 1998 Elsevier Science B.V. Al l rights reserved.