Interval Routing for Generalized Hypercube-Like Graphs

Given a parallel or distributed system, the interconnection network ensures the communication between the processors, the terminal nodes. Each intermediate node has a router, a dedicated co-processor which forwards the messages between processors through the links of the underlying topology. The routers run a distributed algorithm which specifies the way to go from a node of the network to another. This algorithm is described by a routing function. Once a router receives a message, it looks at its header and checks the destination of the message, and finds the output port that will be used to forward the message towards to next intermediate node up to its destination. The output port is a number local to each router and associated to each link between routers. A standard way to implement such algorithms is to use a routing table. To find the output port, the router consults a table which is kept in its local memory. For each destination, this table returns the output port number through which the message can be forwarded. A simple method to organize this table is to associate to each destination the output port number which can serve it. This method is simple, but it is very memory expensive. It requires O(n logd) bits to maintain the routing table in each node of degree d, n being the number of nodes of the underlying graph representing the network. For a large or growing network, this method is not feasible. It is interesting to look for another method in order to reduce the size of the data structure stored by the routers, and used for the routing task. In the field of compact routing, several methods and strategies were introduced to reduce the router memory size, as separator-based strategies routing schemes [FJ86, FJ90], hierarchical routing schemes [PU89, ABNLP89], prefix routing [BTvL90], boolean routing [FG97], and interval routing [SK85, vLT87]. We focus our work on this last technique that offer a more compact data structure for routing tables.