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Online Flow Time Minimization with Gradually Revealed Jobs

Authors Alexander Lindermayr , Guido Schäfer , Jens Schlöter , Leen Stougie

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LIPIcs.ESA.2026.128.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
Keywords
  • optimization
  • scheduling
  • online algorithms
  • competitive analysis
  • flow time
  • non-clairvoyance

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Abstract

We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT) algorithm is optimal. In practice, however, exact processing times are often unknown. At the opposite extreme, non-clairvoyant scheduling, in which processing times are revealed only upon completion, suffers from strong lower bounds on the competitive ratio. This motivates the study of intermediate information models. We introduce a new model in which processing times are revealed gradually during execution. Each job consists of a sequence of operations, and the processing time of an operation becomes known only after the preceding one completes. This models many scheduling scenarios that arise in computing systems.
Our main result is a deterministic O(m²)-competitive algorithm, where m is the maximum number of operations per job. More specifically, we prove a refined competitive ratio in O(m₁ ⋅ m₂), where m₁ and m₂ are instance-dependent parameters describing the operation size structure. Our algorithm and analysis build on recent advancements in robust flow time minimization (SODA '26), where jobs arrive with estimated sizes. However, in our setting we have no bounded estimate on a job’s processing time. Thus, we design a highly adaptive algorithm that gradually explores a job’s operations while working on them, and groups them into virtual chunks whose size can be well-estimated. This is a crucial ingredient of our result and requires a much more careful analysis compared to the robust setting. We also provide lower bounds showing that our bounds are essentially best possible. For the special case of scheduling with uniform obligatory tests, we show that SRPT at the operation level is 2-competitive, which is best possible.

Cite As Get BibTex

Alexander Lindermayr, Guido Schäfer, Jens Schlöter, and Leen Stougie. Online Flow Time Minimization with Gradually Revealed Jobs. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 128:1-128:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.128

Author Details

Alexander Lindermayr
  • Institut für Mathematik, Technische Universität Berlin, Germany
Guido Schäfer
  • Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
  • University of Amsterdam, The Netherlands
Jens Schlöter
  • Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
Leen Stougie
  • Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands
  • Vrije Universiteit Amsterdam, The Netherlands

Funding

  • Lindermayr, Alexander: The main part of this work was done while the author was a research fellow at the Simons Institute for the Theory of Computing for the program on "Algorithmic Foundations for Emerging Computing Technologies" in Fall 2025.
  • Schlöter, Jens: Supported by the Netherlands Organisation for Scientific Research (NWO) through project OCENW.GROOT.2019.015 "Optimization for and with Machine Learning (OPTIMAL)".
  • Stougie, Leen: Supported in part by the Netherlands Organisation for Scientific Research (NWO) through project OCENW.GROOT.2019.015 "Optimization for and with Machine Learning (OPTIMAL)" and Gravitation-project NETWORKS-024.002.003.

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