Fast Exact Algorithms for Survivable Network Design with Uniform Requirements

Agrawal, Akanksha and Misra, Pranabendu and Panolan, Fahad and Saurabh, Saket (2022) Fast Exact Algorithms for Survivable Network Design with Uniform Requirements. Algorithmica. ISSN 0178-4617

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Abstract

We design exact algorithms for the following two problems in survivable network design: (i) designing a minimum cost network with a desired value of edge connectivity, which is called Minimum Weightλ-connected Spanning Subgraph and (ii) augmenting a given network to a desired value of edge connectivity at a minimum cost which is called Minimum Weightλ-connectivity Augmentation. It is easy to see that a minimum solution to these problems contains at most 2 λ(n- 1) edges. Using this fact one can design a brute-force algorithm which runs in time 2 O(λnlogn), however no better algorithms were known previously. In this paper, we give the first single exponential time algorithm for these problems, i.e. running in time 2 O(λn), for both undirected and directed networks. Our results are obtained via well known characterizations of λ-connected graphs, their connections to linear matroids and the recently developed technique of dynamic programming with representative sets. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

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