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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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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

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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)


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
  • 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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