Broadcasting and Scattering in Cube-connected Cycles and Butterfly Networks

The process of sending a message from one node of a communication network to all other nodes is called broadcasting when the message is the same for all nodes and scattering when each of the nodes receives a different message. In this thesis we prove several upper bounds on the time to broadcast and scatter in the Cube-Connected Cycles (CCCd) and Butterfly (BFd) interconnection networks. We use the linear cost model of communication, in which the time to send a single message from one node to its neighbour is the sum of the time to establish the connection and the time to send the data proportional to the length of the message. Our algorithms use pipelining in parallel along several disjoint (spanning) trees. We show how to construct 2 arc-disjoint spanning trees of depths 2d + Ld/2 J + 2 and 3 arc-disjoint spanning trees of depths 3d + 3 in CCCd, and 2 and 4 arc-disjoint spanning trees in BFd, of depths d + Ld/2] + 1 and 2d + 1 respectively, and compare the broadcasting times for different lengths of the broadcasted message. Our scattering algorithms consist of two phases. During the first phase we scatter along perfectly balanced binary subtrees of CCCd and BFd. In the second phase we scatter in parallel in all cycles of CCCd and BFd using several originators. The times to scatter are close to the existing lower bounds for both graphs. AIgorithms are presented for fullduplex and half-duplex links and processor-bound and link-bound communication.