Brief Announcement: Local Deal-Agreement Based Monotonic Distributed Algorithms for Load Balancing in General Graphs

Abstract

In computer networks, participants may cooperate in processing tasks, balancing working loads among them. The distributed load balancing problem is well-known. We present local algorithms solving it based on a short deal-agreement communication. Unlike the previous algorithms, they converge monotonically, always providing a better feasible state as the execution progresses. Our synchronous algorithms achieve $\epsilon$-Balanced state for the continuous setting in time $O(n D \log (n K/\epsilon ))$ and 1-Balanced state for the discrete setting in time $O(n D \log (n K/D) + n D^2)$, for general graphs in the worst case, where n is the number of nodes, K is the initial discrepancy, and D is the graph diameter. We also suggest an asynchronous load balancing algorithm solving the problem in time $O(n K^2)$ for general graphs, and its self-stabilizing version.

This research was (partially) funded by the Office of the Israel Innovation Authority of the Israel Ministry of Economy under Genesis generic research project, the Rita Altura trust chair in computer science, and by the Lynne and William Frankel Center for Computer Science.