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Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing

Authors Chandra Chekuri, Rhea Jain

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Author Details

Chandra Chekuri
  • University of Illinois, Urbana-Champaign, IL, USA
Rhea Jain
  • University of Illinois, Urbana-Champaign, IL, USA

Funding

Chandra Chekuri and Rhea Jain are partially supported by NSF grants CCF-1910149 and CCF-1907937.

Acknowledgements

We thank Mik Zlatin for helpful discussions on hop-constrained metric embeddings.

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Chandra Chekuri and Rhea Jain. Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.41

Abstract

We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results. We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [Chekuri et al., 2010; Guy Kortsarz and Zeev Nutov, 2011]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [Chekuri et al., 2010]. The rounding is based on recent results in hop-constrained oblivious routing [Ghaffari et al., 2021], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to h-hop constrained network design for which we obtain LP-based bicriteria approximation algorithms. We also consider a fault-tolerant version of h-hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [Luis Gouveia and Markus Leitner, 2017; Gouveia et al., 2018; Arslan et al., 2020] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail.

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
  • Theory of computation → Routing and network design problems
Keywords
  • Buy-at-bulk
  • Hop-constrained network design
  • LP integrality gap
  • Fault-tolerant network design

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