Quasirandom Load Balancing

TL;DR

This paper introduces a deterministic quasirandom algorithm for load balancing on graphs that closely approximates ideal divisible token distribution, outperforming previous randomized and deterministic methods in terms of deviation and smoothness.

Contribution

The paper presents a novel quasirandom load balancing algorithm that achieves near-optimal deviation from the ideal process on various network topologies, improving over prior randomized and deterministic approaches.

Findings

On d-dimensional tori, deviation is only an additive constant.

Outperforms previous algorithms with deviations up to Omega(polylog(n)) or Omega(n^{1/d}).

Achieves optimal time and smoothness in load balancing.

Abstract

We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small as possible. Our new algorithm surprisingly closely approximates the idealized process (where the tokens are divisible) on important network topologies. On d-dimensional torus graphs with n nodes it deviates from the idealized process only by an additive constant. In contrast to that, the randomized rounding approach of Friedrich and Sauerwald (2009) can deviate up to Omega(polylog(n)) and the deterministic algorithm of Rabani, Sinclair and Wanka (1998) has a deviation of Omega(n^{1/d}). This makes our quasirandom algorithm the first known algorithm for this setting which is optimal both in time and achieved smoothness. We further show that also on the hypercube our algorithm has a smaller deviation from the idealized process than the previous algorithms.