Periodic Gossiping in Commuted Networks

In this paper we deal with global communication schemes such as broadcasting or multicasting, in a packet (sub)network in which each node participates in the same distributed application. We want the communication scheme to be performed periodically as often as possible and with some bandwidth guarantee. Such periodicity properties are needed, for example, by multimedia and grid computation applications. We consider commuted switches in the network, i.e., each outgoing link of the switch is assigned to at most one incoming link. Each switch avoids intermediate buffering. Given a network G and a global communication scheme S, an algorithm performing S in G consists in commuting each switch and in specifying to each emitting node the infinite sequence of steps at which it will send a message. The period of this algorithm is the greatest number of steps between two messages emitted by a node. The window of the algorithm is the maximal number of steps needed by a message to reach its destination(s). We first give a general definition of the model of network we consider and of the global communication schemes we study, i.e., the many-to-all scheme where many nodes have one message to send to all the other ones. One well-known case of the many-to-all scheme we especially focus on is gossiping. We present a general way of periodically performing these communication schemes, by covering the graph by substructures called octopuses. Then we show that optimizing the period and the windoware two different problems.We end by giving some examples of applications in the torus network.