A polylogarithmic approximation algorithm for 2-edge-connected dominating set

Amir Belgi; Zeev Nutov

doi:10.1016/j.ipl.2021.106175

A polylogarithmic approximation algorithm for 2-edge-connected dominating set

Amir Belgi, Zeev Nutov

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

In the CONNECTED DOMINATING SET (CDS) problem we are given a graph G and seek a min-size dominating set S such that the subgraph G[S] of G induced by S is connected. In the 2-EDGE-CONNECTED DOMINATING SET problem G[S] should be 2-edge-connected. We give the first non-trivial approximation algorithm for this problem, with expected approximation ratio O(log²⁡n⋅log⁡log⁡n⋅(log⁡log⁡log⁡n)³). We also show that the SUBSET STEINER CDS problem is approximation equivalent to the GROUP STEINER TREE problem.

Original language	English
Article number	106175
Journal	Information Processing Letters
Volume	173
DOIs	https://doi.org/10.1016/j.ipl.2021.106175
State	Published - Jan 2022

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Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

2-edge-connected
Approximation algorithms
Dominating set

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10.1016/j.ipl.2021.106175

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title = "A polylogarithmic approximation algorithm for 2-edge-connected dominating set",

abstract = "In the CONNECTED DOMINATING SET (CDS) problem we are given a graph G and seek a min-size dominating set S such that the subgraph G[S] of G induced by S is connected. In the 2-EDGE-CONNECTED DOMINATING SET problem G[S] should be 2-edge-connected. We give the first non-trivial approximation algorithm for this problem, with expected approximation ratio O(log2⁡n⋅log⁡log⁡n⋅(log⁡log⁡log⁡n)3). We also show that the SUBSET STEINER CDS problem is approximation equivalent to the GROUP STEINER TREE problem.",

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doi = "10.1016/j.ipl.2021.106175",

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AB - In the CONNECTED DOMINATING SET (CDS) problem we are given a graph G and seek a min-size dominating set S such that the subgraph G[S] of G induced by S is connected. In the 2-EDGE-CONNECTED DOMINATING SET problem G[S] should be 2-edge-connected. We give the first non-trivial approximation algorithm for this problem, with expected approximation ratio O(log2⁡n⋅log⁡log⁡n⋅(log⁡log⁡log⁡n)3). We also show that the SUBSET STEINER CDS problem is approximation equivalent to the GROUP STEINER TREE problem.

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KW - Approximation algorithms

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A polylogarithmic approximation algorithm for 2-edge-connected dominating set

Abstract

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Keywords

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