Efficient algorithms for connection assignment in interconnection networks

This dissertation addresses the problem of assigning connections in interconnection networks. Connection-assignment problem in two different classes of systems is investigated. In a system of the first class, processors are interconnected using a one-sided crosspoint switching network. In this system, we study the problem of assigning connections when faulty crosspoints exist in the network. We provide a complete characterization of the faulty crosspoint networks that can operate in the nonblocking mode. We show that the one-sided crosspoint networks can tolerate as many as 50 percent faulty crosspoints in the rearrangeable mode of operation. Realizing a connection set on a crosspoint network in the presence of an arbitrary fault-set is modeled as a graph matching problem. Two special distributions of faults, namely rectangular and trapezoidal, which allow easy determination of the rearrangeability are also investigated. All results derived in the context of one-sided crosspoint networks are extended to the case of multiple-bus systems. The second class of systems that we consider consists of satellite-switched time-division multiple access (SS/TDMA) systems. Hierarchical switching systems (HSS's) and SS/TDMA systems with variable bandwidth beams are two examples of these systems. We provide efficient algorithms for connection assignment using optimal number of time-slots in these switching systems. We design sequential, parallel and incremental-sequential algorithms for time-slot assignment (TSA) in these switching systems. Our sequential algorithms are asymptotically faster than the existing sequential algorithms, while parallel algorithms for the TSA problem are proposed for the first time in this dissertation. Our sequential and parallel algorithms are based on modeling the TSA problem as the problem of finding a series of maximum-flows in networks. The incremental-sequential algorithm that we design is shown to achieve considerable speed-up over the other algorithms, when traffic demands in consecutive frames overlap to a significant extent. (Copies available exclusively from Micrographics Department, Doheny Library, USC, Los Angeles, CA 90089-0182.)