Minimum connected dominating sets and maximal independent sets in unit disk graphs

Wu, Weili; Du, Hongwei; Jia, Xiaohua; Li, Yingshu; Huang, Scott C.-H.

doi:10.1016/j.tcs.2005.08.037

Cited by 210 publications

(83 citation statements)

References 10 publications

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“…Lemma3: In the unit disk graph, each connection node is adjacent to at most five independent nodes [6].…”

Section: Theoretical Analysismentioning

confidence: 99%

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A Virtual Backbone Construction Algorithm Based on Connected Dominating Set in Wireless Sensor Networks

Shi¹,

Shi²,

Fang³

2014

Proceedings of the 2014 International Conference on Computer, Communications and Information Technology

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-For the lack of the backbone network in wireless sensor networks,this paper proposes a virtual backbone construction algorithm based on connected dominating set in wireless sensor networks(IPCDS).The algorithm gives priority to more energy and closer nodes in the choice of backbone nodes,which makes network life longer and delay smaller.This paper proves that in unit disk graph the connected dominating set generated by the algorithm is at most 7.6opt+1.4,the message complexity and the time complexity are O(n).Simulation results show that the IPCDS algorithm is significantly better than other algorithms.

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“…Lemma3: In the unit disk graph, each connection node is adjacent to at most five independent nodes [6].…”

Section: Theoretical Analysismentioning

confidence: 99%

“…Lemma4: In the unit disk graph, the maximal independent set does not exceed 3.8opt+1.2, where opt is the minimum connected dominating set [6]. Theorem1: The black node set generated by the IPCDS algorithm Step2 is a maximal independent set.…”

Section: Theoretical Analysismentioning

confidence: 99%

A Virtual Backbone Construction Algorithm Based on Connected Dominating Set in Wireless Sensor Networks

Shi¹,

Shi²,

Fang³

2014

Proceedings of the 2014 International Conference on Computer, Communications and Information Technology

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“…In fact, a degree higher than 15 is never necessary: even if we allow degeneracies, there is a way to break ties so that no vertex of a minimum spanning tree has degree larger than 5 [32]. Thus, if a vertex is adjacent to more than 5 vertices of the same color, we can remove one of the edges and replace it by one of equal or smaller length, preserving connectivity.…”

Section: Lemmamentioning

confidence: 99%

Colored Spanning Graphs for Set Visualization

Hurtado

Korman

Kreveld

et al. 2013

Lecture Notes in Computer Science

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Abstract. We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the blue set, red points belong exclusively to the red set, and purple points belong to both sets. A red-blue-purple spanning graph (RBP spanning graph) is a set of edges connecting the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. We study the geometric properties of minimum RBP spanning graphs and the algorithmic problems associated with computing them. Specifically, we show that the general problem can be solved in polynomial time using matroid techniques. In addition, we discuss more efficient algorithms for the case in which points are located on a line or a circle, and also describe a fast ( 1 2 ρ + 1)-approximation algorithm, where ρ is the Steiner ratio.In memoriam : Ferran Hurtado (1951-2014 This paper was initiated during a research visit hosted by Ferran and his group in Barcelona. Following tradition, hours of research were complemented by relaxing evenings with great food and wine. The authors would like to thank Ferran for being a supportive mentor, an inspiring colleague, and a great friend.

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“…The first one is randomized and gives a k-connected k-dominating set with high probability. The second algorithm is another generalization of Wu et al [29]. It is deterministic and is proven to always give a k-connected k-dominating set.…”

Section: Related Workmentioning

confidence: 99%

Incremental Construction of k-Dominating Sets in Wireless Sensor Networks

Couture

Barbeau

Bose

et al. 2006

Lecture Notes in Computer Science

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Given a graph G, a k-dominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a k-dominating set. The algorithm constructs a monotone family of dominating setsis an i-dominating set. For unit disk graphs, the size of each of the resulting i-dominating sets is at most six times the optimal.

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Minimum connected dominating sets and maximal independent sets in unit disk graphs

Cited by 210 publications

References 10 publications

A Virtual Backbone Construction Algorithm Based on Connected Dominating Set in Wireless Sensor Networks

A Virtual Backbone Construction Algorithm Based on Connected Dominating Set in Wireless Sensor Networks

Colored Spanning Graphs for Set Visualization

Incremental Construction of k-Dominating Sets in Wireless Sensor Networks

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