Parallel Scheduling Algorithm based on Complex Coloring for Input-Queued Switches

TL;DR

This paper introduces a parallel scheduling algorithm for input-queued switches using complex coloring, achieving optimal, rearrangeable, and highly efficient scheduling with near 100% throughput and low computational complexity.

Contribution

It presents a novel distributed parallel scheduling algorithm based on complex coloring that is optimal, rearrangeable, and computationally efficient for input-queued switches.

Findings

Achieves near 100% throughput in packet switching.

Runs in $O( ext{log}^2 N)$ time per frame and $O( ext{log} N)$ amortized time per matching.

Provides a robust, adaptive solution for non-uniform traffic patterns.

Abstract

This paper explores the application of a new algebraic method of edge coloring, called complex coloring, to the scheduling problems of input queued switches. The proposed distributed parallel scheduling algorithm possesses two important features: optimality and rearrangeability. Optimality ensures that the algorithm always returns a proper coloring with the minimum number of required colors, and rearrangeability allows partially re-coloring the existing connection patterns if the underlying graph only changes slightly. The running time of the proposed scheduling algorithm is on the order of $O(\log^2 N)$ per frame, and the amortized time complexity, the time to compute a matching per timeslot, is only $O(\log N)$. The scheduling algorithm is highly robust in the face of traffic fluctuations. Since the higher the variable density, the higher the efficiency of the variable elimination process, complex coloring provides a natural adaptive solution to non-uniform input traffic patterns. The proposed scheduling algorithm for packet switching can achieve nearly 100% throughput.