Breaking the <i>O</i>(ln <i>n</i>) Barrier: An Enhanced Approximation Algorithm for Fault-Tolerant Minimum Weight Connected Dominating Set

Zhou, Jiao; Zhang, Zhao; Tang, Shaojie; Huang, Xiaohui; Du, Dingzhu

doi:10.1287/ijoc.2017.0775

Cited by 6 publications

(8 citation statements)

References 29 publications

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“…As for the weighted version of fault-tolerant virtual backbones, Shi et al [20] and Fukunaga [10] independently presented constant approximation algorithms for the MinW(k, m)CDS problem in UDGs. Regarding general graphs, [25] presented an asymptotic 3 ln δ max -approximation algorithm for MinW(1, m)CDSs. However, as explained in the previous section, the analysis in [25] is flawed.…”

Section: Related Workmentioning

confidence: 99%

“…In 1999, Guha and Khuller [11] designed a (1.35+ε) ln napproximation algorithm for MinWCDSs, where n is the number of nodes. This ratio was not improved until 2018, when Zhou et al [25] presented an (H(δ max + m) + 2H(δ max − 1))approximation algorithm for the minimum-weight (1, m)CDS (MinW(1, m)CDS) problem, where δ max is the maximum degree of the graph and H(•) is the Harmonic number. In real applications, δ max might be much smaller than n. However, there is a flaw in their analysis: an inequality in their derivation contains a small error term 1.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we corrected the flaw in [25] using a completely different idea of analysis, and designed an algorithm for the MinW(1, m)CDS problem in a general graph to achieve the improved approximation ratio 2H(δ max + m − 1).…”

Section: Introductionmentioning

confidence: 99%

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Improved Approximation Algorithm for Minimum-Weight $(1,m)$--Connected Dominating Set

Zhou¹,

Ran²,

Zhang³

et al. 2023

Preprint

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The classical minimum connected dominating set (MinCDS) problem aims to find a minimum-size subset of connected nodes in a network such that every other node has at least one neighbor in the subset. This problem is drawing considerable attention in the field of wireless sensor networks because connected dominating sets can serve as virtual backbones of such networks. Considering fault-tolerance, researchers developed the minimum k-connected m-fold CDS (Min(k, m)CDS) problem. Many studies have been conducted on MinCDSs, especially those in unit disk graphs. However, for the minimum-weight CDS (MinWCDS) problem in general graphs, algorithms with guaranteed approximation ratios are rare. Guha and Khuller designed a (1.35+ε) ln n-approximation algorithm for MinWCDS, where n is the number of nodes. In this paper, we improved the approximation ratio to 2H(δ max + m − 1) for MinW(1, m)CDS, where δ max is the maximum degree of the graph.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Approximation Algorithm for Minimum-Weight $(1,m)$--Connected Dominating Set

Zhou¹,

Ran²,

Zhang³

et al. 2023

Preprint

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“…Due to the importance of coping with failures, the fault tolerance of many additional fundamental problems has been extensively studied. Prime examples are replacement paths [1,21,22,30,54], BFS trees [33,48,[50][51][52], spanners [15-17, 25, 41, 47, 55], connected dominating sets [18,59], and more [8-10, 14, 23, 32, 36, 57] Fault tolerance was also studied in the distributed setting, such as for BFS trees [28], MST [28], and spanners [25,49].…”

Section: Related Workmentioning

confidence: 99%

“…Typically, the focus of fault tolerance has been network design problems, e.g., BFS [33,48,[50][51][52] and spanners [15-17, 25, 41, 47, 55]. Additional related algorithmic problems for which fault tolerant algorithms were studied include, e.g., single source reachability [9,10], connected dominating set [18,59], and facility location [23,32,36,57].…”

Section: Introductionmentioning

confidence: 99%

Fault Tolerant Max-Cut

Censor-Hillel,

Marelly,

Schwartz

et al. 2021

Preprint

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In this work, we initiate the study of fault tolerant Max-Cut, where given an edge-weighted undirected graph G = (V, E), the goal is to find a cut S ⊆ V that maximizes the total weight of edges that cross S even after an adversary removes k vertices from G. We consider two types of adversaries: an adaptive adversary that sees the outcome of the random coin tosses used by the algorithm, and an oblivious adversary that does not. For any constant number of failures k we present an approximation of (0.878 − ) against an adaptive adversary and of α GW ≈ 0.8786 against an oblivious adversary (here α GW is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. ACM '95]). Additionally, we present a hardness of approximation of α GW against both types of adversaries, rendering our results (virtually) tight.The non-linear nature of the fault tolerant objective makes the design and analysis of algorithms harder when compared to the classic Max-Cut. Hence, we employ approaches ranging from multiobjective optimization to LP duality and the ellipsoid algorithm to obtain our results.

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Connected domination in maximal outerplanar graphs

Zhuang

2020

Discrete Applied Mathematics

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Breaking the O(ln n) Barrier: An Enhanced Approximation Algorithm for Fault-Tolerant Minimum Weight Connected Dominating Set

Cited by 6 publications

References 29 publications

Improved Approximation Algorithm for Minimum-Weight $(1,m)$--Connected Dominating Set

Improved Approximation Algorithm for Minimum-Weight $(1,m)$--Connected Dominating Set

Fault Tolerant Max-Cut

Connected domination in maximal outerplanar graphs

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