learning-augmented scheduling

This work addresses the restricted assignment scheduling problem—where each job can only be processed on a specified subset of machines and the objective is to minimize the makespan—by proposing the first learning-augmented framework that integrates predictive assignment information. The approach guarantees a worst-case approximation ratio while ensuring performance degrades smoothly with increasing prediction error, and it introduces a parameterized repair mechanism based on makespan estimation. Key contributions include the design of a dual-guarantee scheduling algorithm that is both robust and prediction-aware, a proof that the exact repair problem is W[1]-hard—establishing a parameterized complexity lower bound—and the integration of a moving-load error metric with classical approximation algorithms to achieve a tunable trade-off between prediction quality and computational efficiency.

This work proposes the first learning-augmented approximation algorithm for the NP-hard unrelated machine scheduling problem to minimize makespan (R||C_max), introducing prediction-guided strategies into scheduling and resolving an open question posed by Antoniadis et al. The algorithm leverages predictions about the assignment of “heavy” jobs: when predictions are accurate, it achieves a (1+ε)-approximation; as prediction error increases, its performance degrades smoothly to a 2-approximation, matching the best-known worst-case bound. This trade-off yields theoretically tight robustness guarantees. Empirical evaluations demonstrate the algorithm’s practical effectiveness in real-world scenarios.

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.

This paper studies online interval scheduling and edge-disjoint path allocation on general graphs under imperfect predictions. Given a dynamically arriving sequence of intervals, the objective is to maximize the number of mutually non-overlapping intervals; this is generalized to path allocation on arbitrary graphs. We establish, for the first time, a tight characterization linking prediction error to competitive ratio. Our method integrates online algorithm design, error-sensitive competitive analysis, and empirical evaluation on real-world workloads. We propose an asymptotically optimal trade-off framework that ensures consistency—achieving near-optimal performance when predictions are accurate—and robustness—degrading gracefully to the classical competitive bound under severe prediction errors. We derive matching upper and lower bounds on the error-dependent competitive ratio. Both theoretical guarantees and empirical results demonstrate strong alignment, significantly enhancing the rigor and practicality of learning-augmented online algorithms.

Traditional robust optimization is often overly conservative due to its exclusive focus on worst-case scenarios, limiting its ability to leverage predictive information for improved scheduling performance. This work proposes the first framework that explicitly incorporates predictions as an independent benchmark in robust scheduling, achieving a principled trade-off between consistency—near-optimality under predicted scenarios—and robustness—guaranteed performance under worst-case uncertainty. By developing a consistency–robustness trade-off mechanism and employing duality theory, upper-envelope reductions, and support-function blocks, the paper systematically analyzes scheduling problems under interval, budgeted, and general uncertainty sets. Smooth $(1+1/\lambda, 1+\lambda)$ trade-offs are established for restricted assignment and related machine models, while the impossibility of constant-factor trade-offs is proven for unrelated machines; constant performance guarantees are provided for identical machines.

This work addresses the fundamental challenge in online scheduling of leveraging predictive information to improve performance while bounding the number of job preemptions, thereby balancing latency and scheduling overhead. The authors propose a learning-augmented online scheduling algorithm that, for the first time, provides theoretical guarantees on bounded preemptions for both unrelated parallel machines and speed-scalable machine models. By integrating competitive analysis with error-sensitive design, the algorithm achieves an $O(1)$ competitive ratio with only $O(1)$ preemptions per job when predictions are accurate; the number of preemptions grows logarithmically with prediction error, ensuring robustness and low overhead. Experimental results validate the approach’s efficacy and establish an analytical bridge between latency performance and preemption complexity.

This study addresses the computational bottlenecks in scientific computing arising from the infeasibility of exact algorithms for large-scale problems. Through a systematic evaluation of approximation methods across 118 core algorithmic problems—integrating complexity analysis, taxonomies of approximation algorithms, and historical context—the work presents the first large-scale empirical evidence demonstrating that only approximately 20% of these problems derive substantial benefit from approximation. Notably, one-quarter of exponential-time-hard problems admit polynomial-time approximation schemes, and the adoption of approximation strategies increases the proportion of linear-time solvable problems by 23%. By quantifying the trade-offs between accuracy and efficiency, this research offers theoretical insights to guide the design of AI-driven and high-performance algorithms.

This work investigates the impact of prediction accuracy on the performance of online algorithms under the distributionally robust competitive ratio (DRCR) framework. By integrating machine-learned predictions, we establish that the optimal DRCR is a monotone concave function of prediction accuracy and extend this property to settings with multiple predictions. Leveraging tools from distributionally robust optimization and competitive analysis, we introduce a method to compute the “critical accuracy”—the minimum prediction precision required to outperform the prediction-free benchmark. Focusing on the ski rental problem, we derive explicit conditions on the accuracy needed to achieve a target DRCR and provide an exact solution for this critical threshold, offering both theoretical guarantees and practical guidance for designing prediction-augmented online algorithms.