Fast distributed approximation for TAP and 2-edge-connectivity

Keren Censor-Hillel, Michal Dory

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


The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph G and a spanning tree T for it, and the goal is to augment T with a minimum set of edges Aug from G, such that T ∪ Aug is 2-edge-connected. TAP has been widely studied in the sequential setting. The best known approximation ratio of 2 for the weighted case dates back to the work of Frederickson and JáJá, SICOMP 1981. Recently, a 3/2-approximation was given for the unweighted case by Kortsarz and Nutov, TALG 2016, and recent breakthroughs by Adjiashvili, SODA 2017, and by Fiorini et al., 2017, give approximations better than 2 for bounded weights. In this paper, we provide the first fast distributed approximations for TAP. We present a distributed 2-approximation for weighted TAP which completes in O(h) rounds, where h is the height of T. When h is large, we show a much faster 4-approximation algorithm for the unweighted case, completing in O(D + √ n log∗ n) rounds, where n is the number of vertices and D is the diameter of G. Immediate consequences of our results are an O(D)-round 2-approximation algorithm for the minimum size 2-edge-connected spanning subgraph, which significantly improves upon the running time of previous approximation algorithms, and an O(hMST + √ n log∗ n)-round 3-approximation algorithm for the weighted case, where hMST is the height of the MST of the graph. Additional applications are algorithms for verifying 2-edge-connectivity and for augmenting the connectivity of any connected spanning subgraph to 2. Finally, we complement our study with proving lower bounds for distributed approximations of TAP.

Original languageEnglish
Title of host publication21st International Conference on Principles of Distributed Systems, OPODIS 2017
EditorsJames Aspnes, Joao Leitao, Alysson Bessani, Pascal Felber
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770613
StatePublished - 1 Mar 2018
Externally publishedYes
Event21st International Conference on Principles of Distributed Systems, OPODIS 2017 - Lisboa, Portugal
Duration: 18 Dec 201720 Dec 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference21st International Conference on Principles of Distributed Systems, OPODIS 2017

Bibliographical note

Publisher Copyright:
© 2017 Keren Censor-Hillel and Michal Dory.


  • Approximation algorithms
  • Connectivity augmentation
  • Distributed network design

ASJC Scopus subject areas

  • Software


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