Fault-tolerant multicasting in hypercubes using local safety information

A fully unsafe hypercube according to the global safety can be split into a unique set of maximal safe subcubes. Multicasting in a maximal safe subcube can be completed reliably based on information related to the maximal safe subcube. A time-optimal multicasting exists if (1) the multicast source is locally safe in the minimum subcube that contains the source and destinations (called a multicast subcube), or (2) the spanning subcube between each destination and the source is safe. We show a sufficient condition for the existence of a multicasting is: the multicast subcube is safe or the spanning subcube between the source and each destination is either safe or is contained in a safe subcube. Methods are presented to set up a partial multicast tree when the above sufficient conditions fail. It is shown that effectiveness of the algorithm can be improved drastically using the partial multicast tree setup technique. Extensive simulation results are also presented.