2-Node-Connectivity Network Design

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We consider network design problems in which we are given a graph G= (V, E) with edge costs, and seek a min-cost/size 2-node-connected subgraph G= (V, E) that satisfies a prescribed property. In the Block-Tree Augmentation problem the goal is to augment a tree T by a min-size edge set F⊆ E such that G= T∪ F is 2-node-connected. We break the natural ratio of 2 for this problem and show that it admits approximation ratio 1.91. This result extends to the related Crossing Family Augmentation problem.In the 2-Connected Dominating Set problem G should dominate V. We give the first non-trivial approximation algorithm for this problem, with expected ratio O~ (log4| V| ).In the 2-Connected Quota Subgraph problem we are given node profits p(v) and G should have profit at least a given quota Q. We show expected ratio O~ (log2| V| ), almost matching the best known ratio O(log2| V| ). Our algorithms are very simple, and they combine three main ingredients: 1.A probabilistic spanning tree embedding with distortion O~ (log | V| ) results in a variant of the Block-Tree Augmentation problem.2.An approximation ratio preserving reduction of Block-Tree Augmentation variants to Node Weighted Steiner Tree problems.3.Using existing approximation algorithms for variants of the Node Weighted Steiner Tree problem.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 18th International Workshop, WAOA 2020, Revised Selected Papers
EditorsChristos Kaklamanis, Asaf Levin
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9783030808785
StatePublished - 2021
Event18th International Workshop on Approximation and Online Algorithms, WAOA 2019 - Virtual, Online
Duration: 9 Sep 202010 Sep 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12806 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th International Workshop on Approximation and Online Algorithms, WAOA 2019
CityVirtual, Online

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • 2-connectivity
  • Approximation algorithm
  • Block-tree augmentation
  • Dominating set
  • Symmetric crossing family


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