Xueyan Tang

Peng Chen, Hailiang Zhao, Xueyan Tang et al.

Learning-augmented paging has been extensively studied in recent years. A key advantage over naive ML-based approaches is \emph{bounded robustness}, which guarantees worst-case performance even when predictions are inaccurate, making these algorithms valuable for real-world systems. Prior work achieves robustness bounds of $2H_k + O(1)$ in the randomized setting, leaving a gap to the optimal competitive ratio $H_k$. In this paper, we study how to close this gap. We begin by reviewing online optimality and proving a new property of the latest $H_k$-competitive algorithm, which facilitates our analysis in the learning-augmented setting. Then, we review existing learning-augmented paging algorithms and introduce a unifying primitive, the \emph{relative prediction budget}, which captures the essence of establishing robustness and reveals that prior algorithms either overuse or underutilize predictions. Guided by the above analysis, we develop a new framework that achieves the best-possible robustness up to an additive constant for learning-augmented paging: $H_k + O(1)$. Experiments further demonstrate strong practical performance.

Mozhengfu Liu, Samir Khuller, Xueyan Tang

Motivated by the critical need for energy-efficient scheduling in cloud computing, this paper investigates Span Minimization, a fundamental variant of the well-studied BusyTime problem. In the general BusyTime problem, $n$ jobs characterized by release times, deadlines, and processing times must be partitioned into bundles of capacity $B$, where the objective is to minimize the total active duration of the virtual machines. Span minimization addresses the specific case of unbounded capacity ($B = \infty$), a problem that serves as a vital precursor for achieving high-performance approximation guarantees in more complex scheduling environments. While previous research established a deterministic $2$-approximation for interval jobs and a $3$-approximation for the general BusyTime problem, the online landscape of span minimization remains less explored. In this paper, we focus on the online version of span minimization. We demonstrate that randomization can be leveraged to break the known deterministic competitive barrier of $2$. For uniform-length jobs, we derive a randomized competitive upper bound of $\frac{1}{\ln{2}}\approx 1.443$ and a lower bound of $\frac{\sqrt{3}+1}{2}\approx 1.366$. Furthermore, we show that by introducing the ability to restart jobs, we can achieve an optimal competitive ratio equal to the golden ratio ($ϕ\approx 1.618$). Our results provide new insights into the power of randomization and flexibility in online energy-aware scheduling.