Effective resource allocation has become a critical issue in high-performance computing (HPC) systems. To effectively allocate resources (e.g., CPU/GPU cores), recent studies focus on predicting each workload’s runtime using machine learning and deep learning models. These methods in HPC often suffer from underestimation, as 33–64% of jobs terminate due to wallclock time limits, whereas user-provided estimates achieve 78–99% success. This failure stems from minimizing mean squared error, which biases predictions toward average-case performance and underestimates jobs in high-skewed (i.e., long-tail) runtime distributions. Specifically, HPC workloads exhibit long-tail runtime distributions, with most jobs completing quickly while a small fraction runs for extremely long durations. To overcome these challenges, we introduce an uncertainty-aware runtime prediction (UARP) method based on multi-quantile regression. Our method directly addresses the underestimation problem by quantifying uncertainty by modeling the conditional distribution without distributional assumptions. Our approach uses the highest-quantile (99th) model and the residual model from the median quantile. The 99th model primarily provides conservative bounds and protection against job underestimates, while the residual uncertainty model protects against unpredictable workloads by estimating prediction variance. In particular, the expected predicted error (i.e., uncertainty) from the residual model plays a critical role in our adaptive safety margin calculation. UARP adds a conservative prediction (99th quantile) and an additional safety margin from our formula, enabling our adaptive margin approach specifically tailored to each job’s characteristics. Evaluation on four production HPC systems (SDSC DataStar, KIT FH2, ANL Interpid, KISTI NURION), UARP achieves 92–99% job success rates while maintaining resource utilization within 1–2% of EASY backfilling. Our method deploys with identical parameters across all systems. This parameter-free deployment eliminates the per-system tuning that fixed-margin approaches require. In addition, our approach integrates with existing schedulers through minimal modification, utilizing uncertainty-aware predictions to prevent timeout-based job termination and preserve system efficiency.

In this study, we propose an efficient sorting method for encrypted data using fully homomorphic encryption (FHE). The proposed method extends the existing 2-way sorting method by applying the k-way sorting network for any prime k to reduce the depth in terms of comparison operation from O(log22n) to O(klogk2n), thereby improving performance for k slightly larger than 2, such as k=5. We apply this method to approximate FHE which is widely used due to its efficiency of homomorphic arithmetic operations. In order to build up the k-way sorting network, the k-sorter, which sorts k-numbers with a minimal comparison depth, is used as a building block. The approximate homomorphic comparison, which is the only type of comparison working on approximate FHE, cannot be used for the construction of the k-sorter as it is because the result of the comparison is not binary, unlike the comparison in conventional bit-wise FHEs. To overcome this problem, we propose an efficient k-sorter construction utilizing the features of approximate homomorphic comparison. Also, we propose an efficient construction of a k-way sorting network using cryptographic SIMD operations. To use the proposed method most efficiently, we propose an estimation formula that finds the appropriate k that is expected to reduce the total time cost when the parameters of the approximating comparisons and the performance of the operations provided by the approximate FHE are given. We also show the implementation results of the proposed method, and it shows that sorting 56= 15625 data using 5-way sorting network can be about 23.3% faster than sorting 214= 16384 data using 2-way.