Algorithms for 2-connected network design and flexible Steiner trees with a constant number of terminals

Bansal, Ishan, Cheriyan, Joe, Grout, Logan and Ibrahimpur, Sharat (2023) Algorithms for 2-connected network design and flexible Steiner trees with a constant number of terminals. In: Megow, Nicole and Smith, Adam, (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023. Leibniz International Proceedings in Informatics, LIPIcs. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. ISBN 9783959772969

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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).

Item Type:	Book Section
Official URL:	https://drops.dagstuhl.de/opus/portals/lipics/inde...
Additional Information:	© 2023 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	10 Oct 2023 13:18
Last Modified:	20 Dec 2024 00:20
URI:	http://eprints.lse.ac.uk/id/eprint/120416

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