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Randomized rounding algorithms for large scale unsplittable flow problems

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Abstract

Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and important numbers of commodities. We present and analyze in detail a heuristic based on the linear relaxation of the problem and randomized rounding. We provide empirical evidence that this approach is competitive with state-of-the-art resolution methods either by its scaling performance or by the quality of its solutions. We provide a variation of the heuristic which has the same approximation factor as the state-of-the-art approximation algorithm. We also derive a tighter analysis for the approximation factor of both the variation and the state-of-the-art algorithm. We introduce a new objective function for the unsplittable flow problem and discuss its differences with the classical congestion objective function. Finally, we discuss the gap in practical performance and theoretical guarantees between all the aforementioned algorithms.

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Authors and Affiliations

  1. ISAE-SUPAERO, Université de Toulouse, Toulouse, France

    François Lamothe, Emmanuel Rachelson & Alain Haït

  2. Thalès Alenia Space, Toulouse, France

    Cedric Baudoin

  3. Centre national d’études spatiales (CNES), Toulouse, France

    Jean-Baptiste Dupé

Authors
  1. François Lamothe
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  2. Emmanuel Rachelson
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  3. Alain Haït
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  4. Cedric Baudoin
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  5. Jean-Baptiste Dupé
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Correspondence to François Lamothe.

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Conflict of interest

This work was partially funded by Thales Alenia Space and made in collaboration with several of its members. This work was partially funded by the CNES. Several authors are academically related to ISAE-SUPAERO. The authors declare that they have no conflict of interest. The datasets and the code used in the experimental section of this work are accessible at https://github.com/SuReLI/randomized_rounding_paper_code.

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Lamothe, F., Rachelson, E., Haït, A. et al. Randomized rounding algorithms for large scale unsplittable flow problems. J Heuristics 27, 1081–1110 (2021). https://doi.org/10.1007/s10732-021-09478-w

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  • DOI: https://doi.org/10.1007/s10732-021-09478-w

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