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

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

Research output: Working paper

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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 nO(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.
Original languageEnglish
Place of PublicationIthaca, NY
Publication statusPublished - 12 Mar 2020


  • k-hop Steiner tree
  • Dynamic programming
  • Network design


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