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arXiv · 2603.29451

Improved Approximation Algorithms for Non-Preemptive Throughput Maximization

Alexander Armbruster·Fabrizio Grandoni·Antoine Tinguely·Andreas Wiese
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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.

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Alexander Armbruster, Fabrizio Grandoni, Antoine Tinguely, Andreas Wiese. 2026-03-31. Improved Approximation Algorithms for Non-Preemptive Throughput Maximization. https://arxiv.org/abs/2603.29451

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