Delayed-Clairvoyant Flow Time Scheduling via a Borrow Graph Analysis

2026-02-25

AI Summary

This work addresses online preemptive single-machine scheduling under the α-predictive model, where the processing time of a job is revealed only after it has been processed for an α-fraction of its total duration. The paper presents the first algorithm achieving a competitive ratio of O(1/(1−α)), which smoothly interpolates between the fully clairvoyant (α=0) and fully non-clairvoyant (α→1) extremes. The proposed algorithm integrates the Shortest Remaining Processing Time (SRPT) principle with non-clairvoyant scheduling strategies, and its performance is rigorously analyzed using the Borrow Graph framework. The resulting competitive ratio varies continuously with α and matches the corresponding randomized lower bound, thereby establishing the tightness of the algorithm’s performance guarantee.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Algorithm Configuration

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the problem of preemptively scheduling jobs online over time on a single machine to minimize the total flow time. In the traditional clairvoyant scheduling model, the scheduler learns about the processing time of a job at its arrival, and scheduling at any time the job with the shortest remaining processing time (SRPT) is optimal. In contrast, the practically relevant non-clairvoyant model assumes that the processing time of a job is unknown at its arrival, and is only revealed when it completes. Non-clairvoyant flow time minimization does not admit algorithms with a constant competitive ratio. Consequently, the problem has been studied under speed augmentation (JACM'00) or with predicted processing times (STOC'21, SODA'22) to attain constant guarantees. In this paper, we consider $α$-clairvoyant scheduling, where the scheduler learns the processing time of a job once it completes an $α$-fraction of its processing time. This naturally interpolates between clairvoyant scheduling ($α=0$) and non-clairvoyant scheduling ($α=1$). By elegantly fusing two traditional algorithms, we propose a scheduling rule with a competitive ratio of $\mathcal{O}(\frac{1}{1-α})$ whenever $0 \leq α< 1$. As $α$ increases, our competitive guarantee transitions nicely (up to constants) between the previously established bounds for clairvoyant and non-clairvoyant flow time minimization. We complement this positive result with a tight randomized lower bound.

Problem

• flow time
• online scheduling
• clairvoyant scheduling
• non-clairvoyant scheduling
• competitive ratio

Innovation

• α-clairvoyant scheduling
• flow time minimization
• competitive ratio
• online scheduling
• borrow graph analysis