Minimum time broadcast in faulty star networks

AbstractIn this paper we give new results on the fault-tolerance capabilities of the star graph. We first consider the problem of determining the maximum number r(n) of vertices in a n! vertices star graph Sn such that by removing any set of vertices and/or edges from Sn of cardinality at most r(n) the diameter of Sn does not increase. Subsequently, we give an algorithm for broadcasting a message in Sn in optimal time (the diameter of Sn) 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