TY - GEN

T1 - Fast exact algorithms for survivable network design with uniform requirements

AU - Agrawal, Akanksha

AU - Misra, Pranabendu

AU - Panolan, Fahad

AU - Saurabh, Saket

N1 - Funding Information:
Supported by “Parameterized Approximation” ERC Starting Grant 306992 and “Rigorous Theory of Preprocessing” ERC Advanced Investigator Grant 267959.
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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. Many well known problems such as Minimum Spanning Tree, Hamiltonian Cycle, Minimum 2-Edge Connected Spanning Subgraph and Minimum Equivalent Digraph reduce to these problems in polynomial time. It is easy to see that a minimum solution to these problems contains at most 2λ(n−1) edges. Using this fact one can design a brute-force algorithm which runs in time 2O(λn(log n+log λ)However no better algorithms were known. In this paper, we give the first single exponential time algorithm for these problems, i.e. running in time 2O(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.

AB - 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. Many well known problems such as Minimum Spanning Tree, Hamiltonian Cycle, Minimum 2-Edge Connected Spanning Subgraph and Minimum Equivalent Digraph reduce to these problems in polynomial time. It is easy to see that a minimum solution to these problems contains at most 2λ(n−1) edges. Using this fact one can design a brute-force algorithm which runs in time 2O(λn(log n+log λ)However no better algorithms were known. In this paper, we give the first single exponential time algorithm for these problems, i.e. running in time 2O(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.

UR - http://www.scopus.com/inward/record.url?scp=85025163305&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-62127-2_3

DO - 10.1007/978-3-319-62127-2_3

M3 - Conference contribution

AN - SCOPUS:85025163305

SN - 9783319621265

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 25

EP - 36

BT - Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings

A2 - Ellen, Faith

A2 - Kolokolova, Antonina

A2 - Sack, Jorg-Rudiger

PB - Springer Verlag

T2 - 15th International Symposium on Algorithms and Data Structures, WADS 2017

Y2 - 31 July 2017 through 2 August 2017

ER -