Strong connectivity augmentation is FPT

Kristine Vitting Klinkby*, Pranabendu Misra, Saket Saurabh

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Abstrakt

Augmenting an undirected or a directed graph (digraph) by adding new edges or arcs, to increase its connectivity to a target value, is a fundamental problem in combinatorial optimization and graph theory. In this paper we study the basic problem of augmenting an input digraph to make it strongly connected, which is known as the Strong Connectivity Augmentation problem. Here, the input is a digraph D = (V, A), a set of links L ⊆ V × V, and a positive integer k. The objective is to decide if there exists a subset F ⊆ L, of size at most k, such that D0 = (V, A ∪ F) is strongly connected. We consider the general version of this problem where, additionally, there is a weight function w : L → R+ on the links, and the goal is to find a minimum weight subset F ⊆ L of cardinality at most k, such that D0 = (V, A∪F) is strongly connected. We design an algorithm for this problem that runs in time 2O(k log k)nO(1), thereby showing that it is fixed parameter tractable (FPT). Here, n = |V |. This also resolves an open problem stated by Guo and Uhlmann more than a decade ago [ Networks 56(2): 131-142 (2010)].

OriginalsprogEngelsk
TitelProceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)
RedaktørerDániel Marx
Antal sider16
ForlagAssociation for Computing Machinery
Publikationsdato2021
Sider219-234
ISBN (Elektronisk)9781611976465
DOI
StatusUdgivet - 2021
Begivenhed32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, USA
Varighed: 10. jan. 202113. jan. 2021

Konference

Konference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Land/OmrådeUSA
ByAlexandria, Virtual
Periode10/01/202113/01/2021
SponsorACM Special Interest Group on Algorithms and Computation Theory (SIGACT), SIAM Activity Group on Discrete Mathematics
NavnProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Bibliografisk note

Funding Information:
∗UniversityofBergen, Norway, andUniversityofSouthern Denmark, Odense, Denmark. kristine.knudsen@ii.uib.no †Max-PlanckInstituteforInformatics, SIC,Saarbrucken, Germany.pmisra@mpi-inf.mpg.de ‡TheInstituteofMathematicalSciences, HBNI,Chennai, India, and University of Bergen, Norway. saket@imsc.res.in Saket Saurabhissupportedbyfundingfrom theEuropeanResearchCouncil(ERC) under theEuropeanUnion’sHorizon2020research andinnovation programme(grantagreement No. 819416)andalsoacknowledgesthe supportofSwarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18.

Publisher Copyright:
Copyright © 2021 by SIAM

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