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Constructing Minimum Connected Dominating Set: Algorithmic Approach

G N Purohit, Usha Sharma
2010 International Journal on Applications of Graph Theory In wireless Ad Hoc Networks And sensor Networks  
In this paper we provide an algorithm to find MCDS in UD Graph. It is based on the computation of convex hulls of sensor nodes or vertices.  ...  Connected Dominating Set is popularly used for constructing virtual backbones for broadcasting operation in WSNs. UD Graph is the most suitable model for a wireless sensor network.  ...  We introduce an algorithm to find Minimum Connected Dominating Set (MCDS) for UD Graph based on computation of convex hull of sensor nodes.  ... 
doi:10.5121/jgraphoc.2010.2305 fatcat:poo5vowtnncnfi5dkeshc7wgne

Localized Flooding Backbone Construction for Location Privacy in Sensor Networks

Yingchang Xiang, Dechang Chen, Xiuzhen Cheng, Kai Xing, Min Song
2007 Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007)  
In this paper, we propose to protect location privacy via a flooding backbone, which is modeled by a minimum connected dominating set (MCDS) in unit-disk graphs.  ...  To our best knowledge, this algorithm is the first localized algorithm with a constant performance ratio for CDS construction in unit-disk graphs.  ...  Connecting an MIS In this section, we propose a localized convex-hull based algorithm to connect a maximal independent set S of a unitdisk graph G(V, E).  ... 
doi:10.1109/snpd.2007.405 dblp:conf/snpd/XiangCCXS07 fatcat:gnqs5hfozfaybkn5jw7dzlxlze

A localized backbone renovating algorithm for wireless ad hoc and sensor networks

Kai Xing, Shuo Zhang, Lei Shi, Haojin Zhu, Yuepeng Wang
2013 2013 Proceedings IEEE INFOCOM  
Furthermore, the LBR algorithm has the ability to deal with arbitrary number of node failures and additions in the network. Index Terms-maximal independent set, backbone renovating  ...  According to our theoretical analysis, the proposed algorithm has the ability to renovate the backbone in a purely localized manner with a guaranteed connectivity of the network, while keeping the backbone  ...  Lemma 6.11: Let I be any maximal independent set and opt be any MCDS of a unit-disk graph G. Then |I| ≤ k · |opt| + 1 for |opt| > 1, k ≤ 4.  ... 
doi:10.1109/infcom.2013.6567021 dblp:conf/infocom/XingZSZW13 fatcat:yvdnrkuzyje3jfe4u7yo3wnosa

An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks [chapter]

Christoph Ambühl
2005 Lecture Notes in Computer Science  
For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree.  ...  We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.  ...  A sun is defined by a convex set T from the unit disk, with the additional property that all edges of the convex hull are bounded by 1.  ... 
doi:10.1007/11523468_92 fatcat:mcjt6g5juzfgvl6kzvthxajgui

Determining an Optimal Visualization of Physically Realizable Symbol Maps

Guilherme Kunigami, Pedro Rezende, Cid Souza, Tallys Yunes
2011 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images  
We focus specifically on optimizing the visualization of physically realizable drawings of opaque disks by maximizing the sum of the visible borders of such disks.  ...  Recent work approaches the problem of drawing these symbols algorithmically and defines metrics to be optimized to attain different kinds of drawings.  ...  An arc of A is a maximal connected portion of the boundary that connects two vertices and contains no vertex in its interior.  ... 
doi:10.1109/sibgrapi.2011.12 dblp:conf/sibgrapi/KunigamiRSY11 fatcat:sbjugkcydjhannbkty3nkmoony

Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm

Hervé Brönnimann, Lutz Kettner, Michel Pocchiola, Jack Snoeyink
2006 SIAM journal on computing (Print)  
Our algorithm, presented in Section 3, is based on the greedy flip algorithm of Pocchiola and Vegter for computing the visibility complex of a scene of n convex objects in the plane [40] .  ...  This in turn implies a strong connectivity property that is useful when studying the flip-graph (Section 2.2, see also [47] ).  ...  Acknowledgement We thank Ileana Streinu and the other participants of the NSF-supported Bellairs workshop on pseudo-triangulations for many enjoyable discussions.  ... 
doi:10.1137/050631008 fatcat:6t4t5isr5zg7zacem7pr5rcpoe

Parameterized Complexity of Geometric Problems

P. Giannopoulos, C. Knauer, S. Whitesides
2007 Computer journal  
It includes fixed-parameter tractable problems in graph drawing, geometric graphs, geometric covering and several other areas, together with an overview of the algorithmic techniques used.  ...  This paper surveys parameterized complexity results for hard geometric algorithmic problems.  ...  ACKNOWLEDGEMENTS We would like to thank Mike Fellows for his support, comments and ideas in the course of writing this survey.  ... 
doi:10.1093/comjnl/bxm053 fatcat:ohzdxo2ehbcgrawsgmzdcvz5xq

Efficient sub-5 approximations for minimum dominating sets in unit disk graphs

Guilherme D. da Fonseca, Celina M.H. de Figueiredo, Vinícius G. Pereira de Sá, Raphael C.S. Machado
2014 Theoretical Computer Science  
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks.  ...  Because the minimum dominating set problem for unit disk graphs is NP-hard, numerous approximation algorithms have been proposed in the literature, including some PTAS.  ...  The algorithm computes a maximal independent set, which turns out to be a 5-approximation because unit disk graphs contain no K 1,6 as induced subgraphs.  ... 
doi:10.1016/j.tcs.2014.01.023 fatcat:rbqmky6winh63kh5uj7fbnpn6y

Nearly Constant Approximation for Data Aggregation Scheduling in Wireless Sensor Networks

S. C. -H. Huang, P.-J. Wan, C. T. Vu, Y. Li, F. Yao
2007 IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications  
In this paper, we designed an algorithm based on maximal independent sets which has an latency bound of 23R + ∆ − 18.  ...  Here ∆ contributes to an additive factor instead of a multiplicative one; thus our algorithm is nearly constant approximation and it has a significantly less latency bound than earlier algorithms especially  ...  Therefore, the convex hull of S must be contained in the disk of radius 2.5 centered at u.  ... 
doi:10.1109/infcom.2007.50 dblp:conf/infocom/HuangWVLY07 fatcat:5iwbegwiljgy3joayy3kt2nmn4

Voronoi-Based Improved Algorithm for Connected Coverage Problem in Wireless Sensor Networks [chapter]

Jie Jiang, Zhen Song, Heying Zhang, Wenhua Dou
2005 Lecture Notes in Computer Science  
In this paper, we consider the connected coverage problem and aim to construct a minimal connected cover set that is sufficient for a given query in wireless sensor networks.  ...  For other situations where the CVT algorithm alone cannot guarantee the network connectivity, we design a Steiner minimum tree (SMT) based algorithm to ensure the network connectivity.  ...  When R c < 2R s , we design a Steiner minimum tree (SMT) based algorithm to find the additional sensors needed to make the communication graph induced by the cover set connected.  ... 
doi:10.1007/11596356_25 fatcat:otzqza36jbfx5dh4cpbreazuwe

On Order-independent Semantics of the Similarity Group-By Relational Database Operator [article]

Mingjie Tang, Ruby Y. Tahboub, Walid G. Aref, Qutaibah M. Malluhi, Mourad Ouzzani
2014 arXiv   pre-print
For each of these operators, we provide a sample algorithm that is order-independent.  ...  Using the notion of interval graphs borrowed from graph theory, we prove that, for certain SGB operators, there exist order-independent implementations.  ...  [13] approximates the clique problem for disk-based data sets by finding all three-vertex cliques (i.e., triangles) in the graph.  ... 
arXiv:1412.4303v1 fatcat:lxq3gehlqfhbldvy6wzdpg7nbe

A local O(n2) gathering algorithm

Bastian Degener, Barbara Kempkes, Friedhelm Meyer auf der Heide
2010 Proceedings of the 22nd ACM symposium on Parallelism in algorithms and architectures - SPAA '10  
We consider the case that robots are limited to see only robots within a bounded vicinity and present an algorithm achieving gathering in O(n 2 ) rounds in expectation.  ...  The gathering problem, where n autonomous robots with restricted capabilities are required to meet in a single point of the plane, is widely studied.  ...  the unit disk graph of the robots remains connected.  ... 
doi:10.1145/1810479.1810523 dblp:conf/spaa/DegenerKH10 fatcat:p4svwiio2ra2feqfbms47v6cja

Worst-case performance of rendezvous networks in the presence of adversarial nodes

Hyongju Park, Seth Hutchinson
2013 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems  
In particular, we investigate the performance of the circumcenter algorithm with connectivity maintenance [1]-[3] when one or more adversarial agents act maliciously to maximally disrupt convergence of  ...  To this end, we formulate a performance objective for each adversary node in terms of the circumradii of its cooperative neighbors in a communication graph which does not require omniscience of adversaries  ...  Fig. 3 : 3 A disk graph G disk (r) showing initial positions of agents and their connectivity.  ... 
doi:10.1109/iros.2013.6697165 dblp:conf/iros/ParkH13 fatcat:migsjmmplbfjjgcznp6pkacmym

An output sensitive algorithm for discrete convex hulls

Sariel Har-Peled
1998 Computational geometry  
Given a convex body C in the plane, its discrete hull is C o = ConvexHull(C N £), where £ = Z x g is the integer lattice.  ...  Actually, using known combinatorial bounds, the running time of the algorithm is 0(6(C) 2/3 log ~(C)). In particular, this bound applies when C is a disk.  ...  The author also wishes to thank Gill Barequet and the referees for their comments and suggestions.  ... 
doi:10.1016/s0925-7721(97)00031-x fatcat:purrifejhjfidkmkumhekk2f5a

BOUNDED LENGTH, 2-EDGE AUGMENTATION OF GEOMETRIC PLANAR GRAPHS

EVANGELOS KRANAKIS, DANNY KRIZANC, OSCAR MORALES PONCE, LADISLAV STACHO
2012 Discrete Mathematics, Algorithms and Applications (DMAA)  
We also provide a constant time algorithm that works in location-aware settings to augment a planar graph into a 2-edge connected planar graph with straight-line edges of length bounded by 3 times the  ...  Algorithms for the construction of spanning planar subgraphs of Unit Disk Graphs (UDGs) do not ensure connectivity of the resulting graph under single edge deletion.  ...  Observe that after this process, I is a valid maximal independent set. To create a 2-edge connected planar graph it is enough to connect consecutive vertices in I.  ... 
doi:10.1142/s179383091250036x fatcat:cdqfts4uuneqjgvmbmcvaja7ja
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