A Parallel Complex Coloring Algorithm for Scheduling of Input-Queued Switches

Abstract

This paper explores the scheduling problem of input-queued switches, based on a new algebraic method of edge coloring called complex coloring. The proposed scheduling algorithm possesses three important features inherent from complex coloring: parallelizability, optimality and rearrangeability. Parallelizability makes the algorithm running very fast in a distributed manner, optimality ensures that the algorithm always returns a proper connection pattern with the minimum number of required colors, and rearrangeability allows partially re-scheduling the existing connection patterns if the traffic patterns only changes slightly. The amortized time complexity of the proposed parallel scheduling algorithm, in terms of the time to compute a matching in a timeslot, is $O({\log}N)$ , where $N$ is the switch size. As for the scalability of input-queued switches, due to its low complexity, our algorithm can achieve nearly 100 percent throughput and provide acceptable queuing delay when $N$ is large. Furthermore, the complex coloring method naturally provides an adaptive solution to non-uniform input traffic pattern. Thus, the proposed parallel scheduling algorithm is highly robust in the face of traffic fluctuations.