Analysis of a graph coloring based distributed load balancing algorithm

Abstract

We present the analysis of a distributed load balancing algorithm based on edge coloring of undirected graphs. One version (linear version) can be studied directly using linear system theory. We show that the performance of another version (integer version), which is more realistic in that the loads are integers, can be studied as a perturbation of the linear version. Both versions of our algorithm converge to stable behavior for arbitrary topologies. In the case of the binary n-cube processor network we prove that after n steps of the integer version, for any initial load distribution, each processor has a load not more than n/2 away from the average.