Randomized rounding algorithms for large scale unsplittable flow problems

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...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Authors: Lamothe, François, Rachelson, Emmanuel, Haït, Alain, Baudoin, Cedric, Jean-Baptiste Dupe
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Empirical analysis
Heuristic
Mathematical analysis
Rounding
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.15550