Narrow Results

High bandwidth and low latency switches are commercially available. Using these switches, it becomes possible to build a system area network to interconnect workstations and processor clusters together to provide a cost-effective parallel computing platform. A processor cluster may be a shared-memory multiprocessor or a mesh-connected multicomputer, etc. The interconnection topology on this kind of platform, called switch-based NOWP, is usually irregular. On such systems, multicast is an important collective communication operation. Two steps are involved in a multicast: (1) the source node sends the multicast message to the destinations which are connected to a switch directly or are the leader of a processor cluster, and (2) the leader node of each cluster sends the message to other destinations in the same cluster. In this paper, we propose two unicast-based multicast algorithms. Algorithm Multicast_1 performs those two steps sequentially; while Algorithm Multicast_2 overlaps them. Performance of the two algorithms will be evaluated and compared.

Assume that there are players and an eavesdropper Eve of unlimited computational power and that several pairs of players have shared secret keys beforehand. In a key sharing graph, each vertex corresponds to a player, and each edge corresponds to a secret key shared by the two players corresponding to the ends of the edge. Given a key sharing graph, a player wishes to send a message to another player so that the eavesdropper Eve and any other player can get no information on the message. In this paper, we first give a necessary and sufficient condition on a key sharing graph for the existence of such a unicast protocol. We then extend the condition to the case where a multiple number of players other than the sender and receiver passively collude. We finally give a sufficient condition for the existence of a secure multicast protocol.