Fast Exact Algorithms for Survivable Network Design with Uniform Requirements

• Published in: Algorithmica Vol. 84; no. 9; pp. 2622 - 2641
• Main Authors: Agrawal, Akanksha, Misra, Pranabendu, Panolan, Fahad, Saurabh, Saket
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2022; Springer Nature B.V
• Subjects: Algorithm Analysis and Problem Complexity; Algorithms; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Dynamic programming; Mathematics of Computing; Minimum cost; Minimum weight; Network design; Theory of Computation; Survivable network design; Network augmentation; Exact algorithms
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-022-00959-3

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 Weight λ -connected Spanning Subgraph and (ii) augmenting a given network to a desired value of edge connectivity at a minimum cost which is called Minimum Weight λ -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 ( λ n log n ) , 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 ( λ n ) , 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.