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Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics

Authors Martin Böhm , Ruben Hoeksma , Nicole Megow , Lukas Nölke , Bertrand Simon

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Combinatorial optimization
Keywords
  • k-hop Steiner tree
  • dynamic programming
  • bounded treewidth

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Abstract

We consider the problem of computing a Steiner tree of minimum cost under a k-hop constraint which requires the depth of the tree to be at most k. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time n^O(k). For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if k is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the k-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension and bounded doubling dimension.

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Martin Böhm, Ruben Hoeksma, Nicole Megow, Lukas Nölke, and Bertrand Simon. Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.18

Author Details

Martin Böhm
  • University of Bremen, Germany
Ruben Hoeksma
  • University of Twente, The Netherlands
Nicole Megow
  • University of Bremen, Germany
Lukas Nölke
  • University of Bremen, Germany
Bertrand Simon
  • University of Bremen, Germany

Funding

Partially funded and supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Projects ME 3825/1 and 146371743 - TRR 89 Invasive Computing.

Acknowledgements

We thank Jiří Sgall for discussions on k-hop MST on paths and an anonymous reviewer for pointing us to the connection between highway dimension and doubling dimension.

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