A Competitive Algorithm for Throughput Maximization on Identical Machines
Benjamin Moseley, Kirk Pruhs, Clifford Stein, Rudy Zhou
TL;DR
The paper tackles online throughput maximization on $m$ identical machines under preemption, seeking a constant-competitive deterministic online algorithm for all $m>1$. It partitions jobs by laxity and combines three deterministic policies—LMNY for high-laxity, SRPT for low-laxity non-viable, and MLax for low-laxity viable—into a unifying FinalAlg, with a careful forest-schedule-based analysis to bound performance against the optimum. The key innovations include viability-based scheduling (MLax), a three-way decomposition of the problem, and a structural reduction of Opt to non-migratory forest schedules, enabling tight comparisons without speed augmentation. The main result is a deterministic $O(1)$-competitive algorithm for all $m>1$, holding for $m\ge 48$ with a simple reduction for smaller $m$, thereby resolving a two-decade open question and providing a scalable, deterministic approach to multi-machine throughput maximization in online settings.
Abstract
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on $m$ identical machines. The main result is an $O(1)$ competitive deterministic algorithm for any number of machines $m >1$.