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Graph Scheduling with Group Completion Times

Authors Lars Rohwedder , Leander Schnaars

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LIPIcs.ESA.2026.100.pdf
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ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • Graph Scheduling
  • Approximation Algorithms
  • Iterated Rounding

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Abstract

In the Graph Scheduling problem we schedule a given multiset of edges on discrete time steps, such that at each step the set of edges forms a matching. The goal is to minimize the sum of weighted group completion times, where a group is a set of edges and it completes when the last edge has been scheduled. Two popular variants of this problem are Coflow Scheduling and Data Migration. Our main result is extending a recent iterated rounding approach from Coflow Scheduling, roughly corresponding to the bipartite case, to the general Graph Scheduling problem. This yields an essentially tight (2+ε)-approximation for the asymptotic setting where OPT is assumed to be large. For this we rely on polyhedral techniques from general matching, namely odd-set inequalities, and graph theoretical results on edge colorings in multigraphs. The state-of-the-art approximation algorithm for Data Migration is a (1+ϕ)-approximation that improves when OPT is small. Taking the best of this and our main result, we obtain an improvement of the approximation rate for Data Migration in any regime.

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Lars Rohwedder and Leander Schnaars. Graph Scheduling with Group Completion Times. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 100:1-100:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.100

Author Details

Lars Rohwedder
  • University of Southern Denmark, Odense, Denmark
Leander Schnaars
  • Technical University of Munich, Germany

Funding

  • Rohwedder, Lars: Supported by Dutch Research Council (NWO) project "The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms" [grant number OCEN.W.21.268].
  • Schnaars, Leander: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - GRK 2201/2 - Projektnummer 277991500.

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