9405539 Oruc A formidable problem in constructing high speed networks is the control and routing of a heterogeneous mix and multirate of signals. in general, the speed of a network is determined by (a) the clock rate at which its nodes operate, (b) the bandwidth of the links between its nodes, (c) the amount of congestion at its nodes, (d) the depth of the network, and (e) the time to compute the routes between its nodes. the first two of these factors are technology dependent where clock rates are reaching a point of saturation. Assuming that, in a network of 10^9 nodes, each node can process 10^8 cycles/sec), even without any congestion, it would take several seconds to send a packet between two nodes that are separated by a distance proportional to the number of nodes in the network. Likewise, it would take seconds to send a packet between two nodes on a network whose routing time is linear in the number of its nodes. Obviously, any congestion at the nodes in both cases will aggravate the travel time of packets so that both the diameter (depth) and routing time of any high performance network with a very large number of nodes ought to increase at less than a linear rate with its number of nodes. In constructing low cost, congestion free (nonblocking) networks with logarithmic orders of depths and routing times. While some low-cost nonblocking networks with logarithmic or polylogarithmic depths such as Clos, Cantor and Bassalygo-Pinsker have been reported, these networks cannot be used for broadband networking unless they exhibit efficient and fast routing schemes. Moreover, in the case of latter two networks, it is also open whether they can realize multicast and conference assignments. this project will attempt to resolve these problems by using recursive network construction techniques, and parallel and distributed computation methods. ***
