A near-optimal real-time hardware scheduler for large cardinality crossbar switches

• Authors: Raymond R. Hoare;Zhu Ding;Alex K. Jones
• Venue: Proceedings of the 2006 ACM/IEEE conference on Supercomputing
• Year: 2006

The maximum matching algorithm for bipartite graphs can be used to provide optimal scheduling for crossbar based interconnection networks. Unfortunately, maximum matching requires O(N3) time for an N x N communication system, which has limited its application to real-time network scheduling. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By taking advantage of the inherent parallelism available in custom hardware design, we introduce three Maximum Matching implementations in hardware and show how we can trade design complexity for performance. Specifically, we examine a Pure Logic Scheduler with three dimensions of parallelism, a Matrix Scheduler with two dimensions of parallelism and a Vector Scheduler with one dimension of parallelism. These designs reduce the algorithmic time complexity down to O(1), O(K), and O(KN), respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K = 2N -- 1 steps, our simulation results show that the scheduler can achieve 99% of the optimal schedule when K = 9. We examine hardware and time complexity of these architectures for crossbar sizes of up to N = 1024. Using FPGA synthesis results, we show that a greedy schedule for various sized crossbars, ranging from 8 x 8 to 256 x 256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024 x 1024 the scheduling can be completed in approximately 10 μs with current technology and could reach under 90 ns with future technologies.