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Weighted Chairman Assignment and Flow-Time Scheduling

Authors Siyue Liu , Victor Reis

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Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • prefix discrepancy
  • flow-time scheduling
  • unsplittable flow

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Abstract

Given positive integers m, n, a fractional assignment x ∈ [0,1]^{m × n} and weights d ∈ ℝⁿ_{> 0}, we show that there exists an assignment y ∈ {0,1}^{m × n} so that for every i ∈ [m] and t ∈ [n], 
|∑_{j ∈ [t]} d_j (x_{ij} - y_{ij})| < max_{j ∈ [n]} d_j. 
This generalizes a result of Tijdeman (1973) on the unweighted version, known as the chairman assignment problem. This also confirms a special case of the single-source unsplittable flow conjecture with arc-wise lower and upper bounds due to Morell and Skutella (IPCO 2020). As an application, we consider a scheduling problem where jobs have release times and machines have closing times, and a job can only be scheduled on a machine if it is released before the machine closes. We give a 3-approximation algorithm for maximum flow-time minimization.

Cite As Get BibTex

Siyue Liu and Victor Reis. Weighted Chairman Assignment and Flow-Time Scheduling. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.98

Author Details

Siyue Liu
  • Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA
Victor Reis
  • Microsoft Research, Redmond, WA, USA

Acknowledgements

We would like to thank R. Ravi for numerous discussions. The work was done during an internship of the first author at Microsoft Research.

References

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