Improved Approximation Algorithms for Non-Preemptive Throughput Maximization

2026-03-31

AI Summary

This study addresses the throughput maximization problem for non-preemptive jobs with time windows on both single and multiple machines—a strongly NP-hard scheduling problem. By integrating combinatorial optimization, approximation algorithm design, and pseudo-polynomial time dynamic programming, the authors significantly improve the best-known approximation ratio for the single-machine case from $1.551+\varepsilon$ to $4/3+\varepsilon$, and further refine it to $5/4+\varepsilon$ in pseudo-polynomial time. These results establish the currently best approximation guarantees for this classical scheduling problem and are successfully extended to the multi-machine setting, offering new theoretical insights and algorithmic advances in scheduling under time-window constraints.

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.

Problem

• Throughput Maximization
• Non-Preemptive Scheduling
• Approximation Algorithms
• NP-hard
• Job Scheduling

Innovation

• Throughput Maximization
• Non-Preemptive Scheduling
• Approximation Algorithms
• Pseudo-Polynomial Time
• Identical Machines