Existing methods for routing of interconnection networks are optimized for a small group of well defined topologies. Currently, system owners and system integrators are looking for ways to connect two or more existing topologies into one, and thereby create a unified system out of several subsystems. Such integration of multiple networks is supported through e.g. The subnet routing functionality i InfiniBand. In this paper we show that the routing problem of such integration is unsolved, because the integration of two deadlock-free subsystems may lead to routing deadlock. Thereafter we present a theory and a methodology for combining multiple networks in a deadlock-free manner. Through experiments we show that the methodology is able to connect different classes of pre-defined topologies with a definable number of interconnecting links. We demonstrate that we are able to maintain the original routing strategy in the sub-networks, and still get close to full utilization of the bridging links. Finally we show that the methodology is computationally feasible.

Difference triangle sets have a number of applications in telecommunications. The authors describe a linear programming model for finding improved lower bounds on the size of such sets. Two integer linear programming formulations for finding minimal difference triangle sets are presented. The linear programming relaxation of the second formulation is strengthened with a family of valid inequalities and solved to yield improved lower bounds. Numerical results for selected difference triangle sets are given.>