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Traffic-Oblivious Multi-Commodity Flow Network Design

Authors Markus Chimani , Max Ilsen

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ACM Subject Classification
  • Mathematics of computing → Network flows
  • Mathematics of computing → Approximation algorithms
  • Networks → Network design and planning algorithms
Keywords
  • Multi-commodity flow
  • Digraphs
  • LP-rounding
  • Approximation algorithm

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Abstract

We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph G with edge capacities cap and a retention ratio α ∈ (0,1), find an edge-wise minimum subgraph G' ⊆ G such that for all traffic matrices T routable in G using a multi-commodity flow, α⋅ T is routable in G'. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network.
In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a max(1/α, 2)-approximation based on a surprisingly simple LP-rounding scheme. We also give instances where this worst-case approximation ratio is met and thus prove that our analysis is tight.

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Markus Chimani and Max Ilsen. Traffic-Oblivious Multi-Commodity Flow Network Design. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.19

Author Details

Markus Chimani
  • Theoretical Computer Science, Osnabrück University, Germany
Max Ilsen
  • Theoretical Computer Science, Osnabrück University, Germany

Funding

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) grant 461207633 (CH 897/7-2).

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