Abstract
In large multistage interconnection networks (MINs) supporting multicast (many-to-many) connections, a source-destination(s) connection may be blocked by some other established connection, even if the required destination is not busy. Moreover, switch and/or link faults may prevent servicing a number of connections. Blocking and switch/link faults can therefore significantly degrade the overall network performance in a random access environment. To make the network more robust and less susceptible to blocking, multiple-path MINs have been proposed. However, with multiple-paths MINs, the problem of conflict-free and fault-free path assignment for concurrent multicasts becomes a formidable task. In this paper, we review one serial algorithm that solves the path assignment problem in multi-path fault-tolerant multicast-connected MINs. The time complexity of this algorithm is O(m /spl rho//sup m/), where m is the number of simultaneous multicast requests (sources) and /spl rho/ is the number of alternate paths in the multi-path network. We introduce another serial algorithm for path assignment with time complexity O(m /spl rho//sup 2/spl xi//), where /spl xi/ is the number of edges in the constraint graph specifying the conflict-free and fault-free paths servicing all pairs of multicast connections (sources). A parallel (SIMD) version of the second serial algorithm requiring O(/spl xi/) processors is also presented. This parallel algorithm, with time complexity O(m(/spl rho//sup 4/+log/sub 2//spl xi/)) under the single match assumption, further reduces the execution time of the parallel path assignment problem.