Fast exact algorithms for survivable network design with uniform requirements

Akanksha Agrawal, Pranabendu Misra, Fahad Panolan, Saket Saurabh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

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 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.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
EditorsFaith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
PublisherSpringer Verlag
Pages25-36
Number of pages12
ISBN (Print)9783319621265
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
Duration: 31 Jul 20172 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10389 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th International Symposium on Algorithms and Data Structures, WADS 2017
Country/TerritoryCanada
CitySt. John’s
Period31/07/172/08/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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