Improved distributed approximations for minimum-weight two-edge-connected spanning subgraph

Michal Dory, Mohsen Ghaffari

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


The minimum-weight 2-edge-connected spanning subgraph (2- ECSS) problem is a natural generalization of thewell-studied minimumweight spanning tree (MST) problem, and it has received considerable attention in the area of network design. The latter problem asks for a minimum-weight subgraph with an edge connectivity of 1 between each pair of vertices while the former strengthens this edge-connectivity requirement to 2. Despite this resemblance, the 2-ECSS problem is considerably more complex than MST. While MST admits a linear-time centralized exact algorithm, 2-ECSS is NP-hard and the best known centralized approximation algorithm for it (that runs in polynomial time) gives a 2-approximation. In this paper, we give a deterministic distributed algorithm with round complexity of HO(D+√n) that computes a (9+ϵ)-approximation of 2-ECSS, for any constant ϵ > 0. Up to logarithmic factors, this complexity matches the Ω(D + √n) lower bound that can be derived from the technique of Das Sarma et al. [STOC f11], as shown by Censor-Hillel and Dory [OPODIS f17]. Our result is the first distributed constant approximation for 2-ECSS in the nearly optimal time and it improves on a recent randomized algorithm of Dory [PODC f18], which achieved an O(logn)-approximation in HO(D +√n) rounds. We also present an alternative algorithm forO(logn)-approximation, whose round complexity is linear in the low-congestion shortcut parameter of the network.following a framework introduced by Ghaffari and Haeupler [SODA f16]. This algorithm has round complexity HO(D +√ n) in worst-case networks but it provably runs much faster in many well-behaved graph families of interest. For instance, it runs in HO(D) time in planar networks and those with bounded genus, bounded path-width or bounded tree-width.

Original languageEnglish
Title of host publicationPODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9781450362177
StatePublished - 16 Jul 2019
Externally publishedYes
Event38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada
Duration: 29 Jul 20192 Aug 2019

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference38th ACM Symposium on Principles of Distributed Computing, PODC 2019

Bibliographical note

Publisher Copyright:
© 2019 Association for Computing Machinery. All rights reserved.


  • Approximation algorithms
  • Distributed graph algorithms
  • Distributed network design
  • K-edge-connectivity

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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