Scheduling Traffic Matrices On General Switch Fabrics

A traffic matrix is an |S| times |T| matrix M, where M_ij is a non-negative integer encoding the number of packets to be transferred from source i to sink j. Chang et al. (2001) have shown how to efficiently compute an optimum schedule for transferring packets from sources to sinks when the sources and sinks are connected via a rearrangeable fabric such as crossbar. We address the same problem when the switch fabric is not rearrangeable. Specifically, we (1) prove that the optimum scheduling problem is NP-hard for general switch fabrics, (2) identify a sub-class of fabrics for which the problem is polynomial-time solvable, and (3) develop a heuristic for the general case