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Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals

Authors Ishan Bansal, Joe Cheriyan, Logan Grout, Sharat Ibrahimpur

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Author Details

Ishan Bansal
  • Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA
Joe Cheriyan
  • Department of Combinatorics and Optimization, University of Waterloo, Canada
Logan Grout
  • Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA
Sharat Ibrahimpur
  • Department of Mathematics, London School of Economics and Political Science, UK

Funding

  • Cheriyan, Joe: Supported in part by NSERC, RGPIN-2019-04197.
  • Ibrahimpur, Sharat: Received funding from the following sources: NSERC grant 327620-09 and an NSERC DAS Award, European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. ScaleOpt–757481), and Dutch Research Council NWO Vidi Grant 016.Vidi.189.087.

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Ishan Bansal, Joe Cheriyan, Logan Grout, and Sharat Ibrahimpur. Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.14

Abstract

The k-Steiner-2NCS problem is as follows: Given a constant (positive integer) k, and an undirected connected graph G = (V,E), non-negative costs c on the edges, and a partition (T, V⧵T) of V into a set of terminals, T, and a set of non-terminals (or, Steiner nodes), where |T| = k, find a min-cost two-node connected subgraph that contains the terminals. The k-Steiner-2ECS problem has the same inputs; the algorithmic goal is to find a min-cost two-edge connected subgraph that contains the terminals.
We present a randomized polynomial-time algorithm for the unweighted k-Steiner-2NCS problem, and a randomized FPTAS for the weighted k-Steiner-2NCS problem. We obtain similar results for a capacitated generalization of the k-Steiner-2ECS problem.
Our methods build on results by Björklund, Husfeldt, and Taslaman (SODA 2012) that give a randomized polynomial-time algorithm for the unweighted k-Steiner-cycle problem; this problem has the same inputs as the unweighted k-Steiner-2NCS problem, and the algorithmic goal is to find a min-cost simple cycle C that contains the terminals (C may contain any number of Steiner nodes).

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Approximation algorithms
  • Capacitated network design
  • Network design
  • Parametrized algorithms
  • Steiner cycle problem
  • Steiner 2-edge connected subgraphs
  • Steiner 2-node connected subgraphs

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