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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.14
Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals

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

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

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).
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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)

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@InProceedings{bansal_et_al:LIPIcs.APPROX/RANDOM.2023.14,
  author =	{Bansal, Ishan and Cheriyan, Joe and Grout, Logan and Ibrahimpur, Sharat},
  title =	{{Algorithms for 2-Connected Network Design and Flexible Steiner Trees with a Constant Number of Terminals}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.14},
  URN =		{urn:nbn:de:0030-drops-188396},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.14},
  annote =	{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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