Load Balancing: The Long Road from Theory to Practice

TL;DR

This paper advances the practical application of approximation schemes for scheduling jobs on identical machines, achieving faster solutions with improved guarantees compared to previous algorithms.

Contribution

It refines ILP techniques to develop the fastest known approximation scheme for makespan scheduling, bridging the gap between theoretical algorithms and practical implementation.

Findings

Achieves epsilon values lower than 18.2% within reasonable time

Refines ILP techniques for faster approximation schemes

MULTIFIT has the best proven guarantee among non-scheme algorithms

Abstract

There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but the running time grows exponentially in $1/\epsilon$. For a long time, these schemes seemed like a purely theoretical concept. Even solving instances for moderate values of $\epsilon$ seemed completely illusional. In an effort to bridge theory and practice, we refine recent ILP techniques to develop the fastest known approximation scheme for this problem. An implementation of this algorithm reaches values of $\epsilon$ lower than $2/11\approx 18.2\%$ within a reasonable timespan. This is the approximation guarantee of MULTIFIT, which, to the best of our knowledge, has the best proven guarantee of any non-scheme algorithm.