research-article

A Simplified 1.5-Approximation Algorithm for Augmenting Edge-Connectivity of a Graph from 1 to 2

Authors:

Zeev NutovAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 12, Issue 2

Article No.: 23, Pages 1 - 20

https://doi.org/10.1145/2786981

Published: 17 November 2015 Publication History

Abstract

The Tree Augmentation Problem (TAP) is as follows: given a connected graph G=(V, ε) and an edge set E on V, find a minimum size subset of edges F⊆E such that (V, ε ∪ F) is 2-edge-connected. In the conference version [Even et al. 2001] was sketched a 1.5-approximation algorithm for the problem. Since a full proof was very complex and long, the journal version was cut into two parts. The first part [Even et al. 2009] only proved ratio 1.8. An attempt to simplify the second part produced an error in Even et al. [2011]. Here we give a correct, different, and self-contained proof of the ratio 1.5 that is also substantially simpler and shorter than the previous proofs.

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Cited By

Nutov Z(2024)2-node-connectivity network designTheoretical Computer Science10.1016/j.tcs.2023.114367987(114367)Online publication date: Mar-2024
https://doi.org/10.1016/j.tcs.2023.114367
Cecchetto FTraub VZenklusen R(2024)Better-than--approximations for leaf-to-leaf tree and connectivity augmentationMathematical Programming: Series A and B10.1007/s10107-023-02018-3207:1-2(515-549)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s10107-023-02018-3
Traub VZenklusen RSaha BServedio R(2023)A (1.5+ε)-Approximation Algorithm for Weighted Connectivity AugmentationProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585122(1820-1833)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585122
Show More Cited By

Index Terms

A Simplified 1.5-Approximation Algorithm for Augmenting Edge-Connectivity of a Graph from 1 to 2
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 12, Issue 2

February 2016

385 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2846106

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2015 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 November 2015

Accepted: 01 May 2015

Revised: 01 May 2015

Received: 01 July 2014

Published in TALG Volume 12, Issue 2

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Cited By

Nutov Z(2024)2-node-connectivity network designTheoretical Computer Science10.1016/j.tcs.2023.114367987(114367)Online publication date: Mar-2024
https://doi.org/10.1016/j.tcs.2023.114367
Cecchetto FTraub VZenklusen R(2024)Better-than--approximations for leaf-to-leaf tree and connectivity augmentationMathematical Programming: Series A and B10.1007/s10107-023-02018-3207:1-2(515-549)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s10107-023-02018-3
Traub VZenklusen RSaha BServedio R(2023)A (1.5+ε)-Approximation Algorithm for Weighted Connectivity AugmentationProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585122(1820-1833)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585122
Cheriyan JCummings RDippel JZhu J(2023)An Improved Approximation Algorithm for the Matching Augmentation ProblemSIAM Journal on Discrete Mathematics10.1137/21M145350537:1(163-190)Online publication date: 20-Jan-2023
https://doi.org/10.1137/21M1453505
Cecchetto FTraub VZenklusen R(2023)Bridging the Gap Between Tree and Connectivity Augmentation: Unified and Stronger ApproachesSIAM Journal on Computing10.1137/21M1430601(STOC21-26-STOC21-103)Online publication date: 12-Apr-2023
https://doi.org/10.1137/21M1430601
Byrka JGrandoni FAmeli A(2023)Breaching the 2-Approximation Barrier for Connectivity Augmentation: A Reduction to Steiner TreeSIAM Journal on Computing10.1137/21M142114352:3(718-739)Online publication date: 23-May-2023
https://doi.org/10.1137/21M1421143
Tao BXiao MZhao J(2023)Minimum-Weight Link-Disjoint Paths With a Bounded Number of Shared NodesIEEE Transactions on Network and Service Management10.1109/TNSM.2023.323783220:3(2598-2610)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1109/TNSM.2023.3237832
Grandoni FAmeli ATraub VLeonardi SGupta A(2022)Breaching the 2-approximation barrier for the forest augmentation problemProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520035(1598-1611)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520035
Traub VZenklusen R(2022)A Better-Than-2 Approximation for Weighted Tree Augmentation2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS52979.2021.00010(1-12)Online publication date: Feb-2022
https://doi.org/10.1109/FOCS52979.2021.00010
Iglesias JRavi R(2022)Coloring down: 3/2-approximation for special cases of the weighted tree augmentation problemOperations Research Letters10.1016/j.orl.2022.10.00750:6(693-698)Online publication date: Nov-2022
https://doi.org/10.1016/j.orl.2022.10.007
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