Approximation Algorithms for Domatic Partitions of Unit Disk Graphs

Pandit, Saurav; Pemmaraju, Sriram V.; Varadarajan, Kasturi

doi:10.1007/978-3-642-03685-9_24

Cited by 34 publications

(14 citation statements)

References 13 publications

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“…For large vertex sets (n = 1600, 3200) the resulting backbones are shown to each cover typically over 99% of the vertices of G (i.e. ε < 0.01), with about 30% being fully dominating, which is consistent with the 1 4 constant approximation factor algorithm proposed recently in [23] for the domatic partition problem in Unit Disk Graphs. We establish experimentally by measures of node degrees, link lengths, and interior triangular face counts that each individual backbone has most of the coverage behavior and routing convenience of the triangular "perfect packing" lattice.…”

Section: Introductionsupporting

confidence: 80%

“…The problem of finding the maximum number of disjoint dominating sets in an arbitrary graph is known as the domatic partition problem [6]. The majority of the recent work [6] [10,11] [20,21] [22,23,24][27] focuses on designing centralized and distributed logarithmic or constant factor approximation solutions to the strict domatic partition problem which means the output of the algorithm should be the maximum number of disjoint fully dominating sets, where that maximum is never larger than the minimum degree δ plus one. Some of these works tie in the problem solution to maximizing the clustering or target coverage lifetime in sensor networks [22] [27].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the authors of [23] propose the first constant factor approximation algorithm to the domatic partition problem in Unit Disk Graphs. The theoretical result of [23] comes in accordance with our experimental results published around the same time in [16], where we empirically show by using several graph coloring algorithms in Random Geometric Graphs, better results on the domatic number than the log n approximation factor of [6][22] [27] in arbitrary graphs.…”

Section: Introductionmentioning

confidence: 99%

“…constant approximation factor algorithm proposed recently in [23] for the domatic partition problem in Unit Disk Graphs. We establish experimentally by measures of node degrees, link lengths, and interior triangular face counts that each individual backbone has most of the coverage behavior and routing convenience of the triangular "perfect packing" lattice.…”

mentioning

confidence: 99%

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Employing (1 − ∊) Dominating Set Partitions as Backbones in Wireless Sensor Networks

Mahjoub

Matula

2010

2010 Proceedings of the Twelfth Workshop on Algorithm Engineering and Experiments (ALENEX)

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For a random geometric graph G(n, r) of minimum degree δ, we introduce an efficient algorithm for selecting (δ + 1) backbones with disjoint node sets that are each independent (1 − ε) dominating sets of G. The backbone node sets are determined by a graph coloring algorithm employing only the topology (not the geometry) of G(n, r), and the backbone links are selected with link lengths in a narrow window between r and 2r and further to form a planar graph backbone. For large vertex sets (n = 1600, 3200) the resulting backbones are shown to each cover typically over 99% of the vertices of G (i.e. ε < 0.01), with about 30% being fully dominating, which is consistent with the 1 4 constant approximation factor algorithm proposed recently in [23] for the domatic partition problem in Unit Disk Graphs. We establish experimentally by measures of node degrees, link lengths, and interior triangular face counts that each individual backbone has most of the coverage behavior and routing convenience of the triangular "perfect packing" lattice. We further show for each sample G(n, r) that the relatively few vertices not covered by all (δ + 1) backbones are covered by most of the backbones. Hence backbone rotation in a wireless sensor network would reach all sensors (vertices) sufficiently frequently. Our novel backbone generation algorithm confirms experimentally the existence of these (δ + 1) backbones in a random geometric graph, and provides an efficient topologically based centralized algorithm for determining the backbones. We also point out that our novel backbone construction method is flexible such that any efficient coloring algorithm can be plugged into it. In this paper, we experiment with several coloring algorithms: Smallest Last, Largest First, Lexicographic, Radial Sweep and Random and we compare their respective performance. Our emphasis is, however, on SL since it offers robust properties and interesting expected behavior. We also experiment with several random node distributions: uniform, skewed and normal in both unit square and disk of which we also discuss the results. * Boby B. Lyle School of Engineering. Southern Methodist University. Dallas, TX 75275-0122, USA.

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Section: Introductionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Employing (1 − ∊) Dominating Set Partitions as Backbones in Wireless Sensor Networks

Mahjoub

Matula

2010

2010 Proceedings of the Twelfth Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…Pandit, Pemmaraju and Varadarajan [9] consider a special case where the point set that needs to be covered is the same as the centers of the given disks. For this version of the problem, better known as the domatic partition problem for unit disk graphs [10], they show that it is possible to compute Ω(k) disjoint covers.…”

Section: Introductionmentioning

confidence: 99%