A LOCAL Constant Approximation Factor Algorithm for Minimum Dominating Set of Certain Planar Graphs

Alipour, Sharareh; Jafari, Amir

doi:10.1145/3350755.3400217

Cited by 10 publications

(13 citation statements)

References 2 publications

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“…In this paper we propose a local approximation algorithm which is an extension of [2]. We prove that the approximation factor of this algorithm in planar triangle free graphs is 16 and 32 for MTDS problem and MDS problem, respectively.…”

Section: Our Resultsmentioning

confidence: 99%

“…However, there exist an algorithm with approximation factor of 52 for computing a MDS in planar graphs [10,20] in local model and an algorithm with approximation factor of 636 for anonymous networks [10,31]. In [2], they improved the approximation factor in anonymous networks to 18 in planar graphs without 4-cycles. For more information on local algorithms see [27].…”

Section: Previous Workmentioning

confidence: 99%

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On Distributed Algorithms for Minimum Dominating Set problem, from theory to application

Alipour¹,

Futuhi²,

Karimi³

2020

Preprint

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In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact answer. This problem arises naturally in social networks, for example in news spreading, avoiding rumor spreading and recommendation spreading. So we implement our algorithm on massive social networks and compare our results with the state of the art algorithms. Also, we extend our algorithm to solve the -distance dominating set problem and experimentally study the efficiency of the proposed algorithm.Our proposed algorithm is fast and easy to implement and can be used in dynamic networks where the edges and vertices are added or deleted constantly. More importantly, based on the experimental results the proposed algorithm has reasonable solutions and running time which enables us to use it in distributed model practically.

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Section: Our Resultsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

On Distributed Algorithms for Minimum Dominating Set problem, from theory to application

Alipour¹,

Futuhi²,

Karimi³

2020

Preprint

Self Cite

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“…We believe that 5 is the right answer. In the second case, an 18-approximation is known [4], and there is no non-trivial lower bound. We refrain from conjecturing the right bound here -we simply point out that there is no reason yet to think 3 is out of reach.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we focus instead on restricted subclasses of planar graphs. Better approximation ratios can be obtained with additional structural assumptions: 32 if the planar graph contains no triangle [3] and 18 if the planar graph contains no cycle of length four [4]. These bounds are not tight, and in fact we expect they can be improved significantly.…”

Section: Introductionmentioning

confidence: 99%

A tight local algorithm for the minimum dominating set problem in outerplanar graphs

Bonamy¹,

Cook²,

Groenland³

et al. 2021

Preprint

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We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a (5 − ε)-approximation, for any ε > 0. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.

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“…Better approximation ratios are known for some special cases, e.g. 32 if the planar graph is triangle-free [1, Theorem 2.1], 18 if the planar graph has girth five [2] and 5 if the graph is outerplanar (and this bound is tight) [4, Theorem 1].…”

Section: Introductionmentioning

confidence: 99%

Local planar domination revisited

Ozan¹,

Siebertz²,

Vigny³

2021

Preprint

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We show how to compute a 20 -approximation of a minimum dominating set in a planar graph in a constant number of rounds in the LOCAL model of distributed computing. This improves on the previously best known approximation factor of 52, which was achieved by an elegant and simple algorithm of Lenzen et al. Our algorithm combines ideas from the algorithm of Lenzen et al. with recent work of Czygrinow et al. and Kublenz et al. to reduce to the case of bounded degree graphs, where we can simulate a distributed version of the classical greedy algorithm.

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A LOCAL Constant Approximation Factor Algorithm for Minimum Dominating Set of Certain Planar Graphs

Cited by 10 publications

References 2 publications

On Distributed Algorithms for Minimum Dominating Set problem, from theory to application

On Distributed Algorithms for Minimum Dominating Set problem, from theory to application

A tight local algorithm for the minimum dominating set problem in outerplanar graphs

Local planar domination revisited

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