Improved Approximation Algorithms for Non-Preemptive Throughput Maximization

TL;DR

This paper presents improved approximation algorithms for the NP-hard non-preemptive throughput maximization scheduling problem, achieving ratios of 4/3+ε and 5/4+ε with different computational complexities.

Contribution

The authors develop significantly better approximation algorithms for non-preemptive scheduling, improving the best-known ratios from about 1.55 to 4/3+ε and 5/4+ε.

Findings

Achieved approximation ratio of 4/3+ε for the problem.

Further improved to 5/4+ε using pseudo-polynomial algorithms.

Results extend to multiple identical machines.

Abstract

The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$, during which~$j$ can be scheduled. Our goal is to schedule the maximum possible number of jobs non-preemptively on a single machine, so that no two scheduled jobs are processed at the same time. This problem is known to be strongly NP-hard. The best-known approximation algorithm for it has an approximation ratio of $1/0.6448 + \varepsilon \approx 1.551 + \varepsilon$ [Im, Li, Moseley IPCO'17], improving on an earlier result in [Chuzhoy, Ostrovsky, Rabani FOCS'01]. In this paper we substantially improve the approximation factor for the problem to $4/3+\varepsilon$ for any constant~$\varepsilon>0$. Using pseudo-polynomial time $(nT)^{O(1)}$, we improve the factor even further to $5/4+\varepsilon$. Our results extend to the setting in which we are given an arbitrary number of (identical) machines.