Liar’s Dominating Set in Unit Disk Graphs

Jallu, Ramesh K.; Jena, Sangram K.; Das, Gautam

doi:10.1007/978-3-319-94776-1_43

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…for each pair of points p i , p j ∈ P, |(N [p i ] ∪ N [p j ]) ∩ D| ≥ 3. Jallu et al [9] studied the LDS problem on unit disk graphs, and proved that this problem is NP-complete. Furthermore, given an unit disk graph G = (V, E) and an > 0, they have designed a (1+ )-factor approximation algorithm to find an LDS in G with running time n O(c 2 ) , where c = O( 1 log 1 ).…”

Section: Approximation Algorithm For Lds On Unit Disk Graphsmentioning

confidence: 99%

Algorithm and Hardness Results on Liar’s Dominating Set and $$\varvec{k}$$-tuple Dominating Set

Banerjee

Bhore²

2019

Lecture Notes in Computer Science

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Given a graph G = (V, E), the dominating set problem asks for a minimum subset of vertices D ⊆ V such that every vertex u ∈ V \D is adjacent to at least one vertex v ∈ D. That is, the set D satisfies the condition that |NIn this paper, we study two variants of the classical dominating set problem: k-tuple dominating set (k-DS) problem and Liar's dominating set (LDS) problem, and obtain several algorithmic and hardness results.On the algorithmic side, we present a constant factor ( 11 2 )-approximation algorithm for the Liar's dominating set problem on unit disk graphs. Then, we obtain a PTAS for the k-tuple dominating set problem on unit disk graphs. On the hardness side, we show a Ω(n 2 ) bits lower bound for the space complexity of any (randomized) streaming algorithm for Liar's dominating set problem as well as for the k-tuple dominating set problem. Furthermore, we prove that the Liar's dominating set problem on bipartite graphs is W[2]-hard.

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Section: Approximation Algorithm For Lds On Unit Disk Graphsmentioning

confidence: 99%

Algorithm and Hardness Results on Liar’s Dominating Set and $$\varvec{k}$$-tuple Dominating Set

Banerjee

Bhore²

2019

Lecture Notes in Computer Science

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“…communication networks [1], locating servers [2] and copying a distributed directory [3]. There are various types of L-MDS problem, such as Liar's dominating set [4], the extended dominating set [5], the 2-distance paired dominating set [6], the [1, 2]dominating set [7], the (σ, ρ ) dominating set [8], and the k-tuple dominating set [9]. The DMDS has wide application in the field of biological networks, such as for the spread of infectious disease [10], genetic regulation [11,12] and chemical reactions and metabolic regulation [13], and it is also applied in social, information and neuroscience fields [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of the directed 2-distance minimal dominating set problem

Habibulla¹

2020

Commun. Theor. Phys.

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The directed L-distance minimal dominating set (MDS) problem has wide practical applications in the fields of computer science and communication networks. Here, we study this problem from the perspective of purely theoretical interest. We only give results for an Erdós Rényi (ER) random graph and regular random (RR) graph, but this work can be extended to any type of network. We develop spin glass theory to study the directed 2-distance MDS problem. First, we find that the belief propagation (BP) algorithm does not converge when the inverse temperature β exceeds a threshold on either an ER random network or RR network. Second, the entropy density of replica symmetric theory has a transition point at a finite β on a regular random graph when the arc density exceeds 2 and on an ER random graph when the arc density exceeds 3.3; there is no entropy transition point (or ) in other circumstances. Third, the results of the replica symmetry (RS) theory are in agreement with those of BP algorithm while the results of the BP decimation algorithm are better than those of the greedy heuristic algorithm.

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Liar’s dominating set problem on unit disk graphs

Jallu

Das

2020

Discrete Applied Mathematics

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Liar’s Dominating Set in Unit Disk Graphs

Cited by 3 publications

References 14 publications

Algorithm and Hardness Results on Liar’s Dominating Set and $$\varvec{k}$$-tuple Dominating Set

Algorithm and Hardness Results on Liar’s Dominating Set and $$\varvec{k}$$-tuple Dominating Set

Statistical mechanics of the directed 2-distance minimal dominating set problem

Liar’s dominating set problem on unit disk graphs

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