On the Complexity of Load Balancing in Dynamic Networks

TL;DR

This paper investigates the time complexity of load balancing in dynamic networks, presenting a deterministic algorithm, proving limitations for integral loads, and applying smoothed analysis to suggest faster real-world performance.

Contribution

It introduces a deterministic load balancing algorithm, proves bounds for integral loads, and uses smoothed analysis to challenge existing complexity lower bounds.

Findings

Deterministic algorithm slightly improves previous running time.

No matching-based algorithm can bound convergence time for integral loads.

Smoothed analysis indicates real-world load balancing may be faster than theoretical lower bounds.

Abstract

In the load balancing problem, each node in a network is assigned a load, and the goal is to equally distribute the loads among the nodes, by preforming local load exchanges. While load balancing was extensively studied in static networks, only recently a load balancing algorithm for dynamic networks with a bounded convergence time was presented. In this paper, we further study the time complexity of load balancing in the context of dynamic networks. First, we show that randomness is not necessary, and present a deterministic algorithm which slightly improves the running time of the previous algorithm, at the price of not being matching-based. Then, we consider integral loads, i.e., loads that cannot be split indefinitely, and prove that no matching-based algorithm can have a bounded convergence time for this case. To circumvent both this impossibility result, and a known one for the non-integral case, we apply the method of smoothed analysis, where random perturbations are made over the worst-case choices of network topologies. We show both impossibility results do not hold under this kind of analysis, suggesting that load-balancing in real world systems might be faster than the lower bounds suggest.