Fast Exact Algorithms for Survivable Network Design with Uniform Requirements

Akanksha Agrawal, Pranabendu Misra, Fahad Panolan, Saket Saurabh

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2622-2641
Number of pages20
JournalAlgorithmica
Volume84
Issue number9
DOIs
StatePublished - 1 Sep 2022
Externally publishedYes

Keywords

  • Exact algorithms
  • Network augmentation
  • Survivable network design

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics

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