Full-Coverage and k-Connectivity (k=14,6) Three Dimensional Networks

In this paper, we study the problem of constructing full-coverage three dimensional networks with multiple connectivity. We design a set of patterns for full coverage and two representative connectivity requirements, i.e. 14- and 6-connectivity. We prove their optimality under any ratio of the communication range over the sensing range among regular lattice deployment patterns. We also conduct a study on the proposed patterns under practical settings. To our knowledge, our work is the first one that provides deployment patterns with proven optimality that achieve both coverage and connectivity in three dimensional networks.

[1]  M.K. Watfa,et al.  A coverage algorithm in 3D wireless sensor networks , 2006, 2006 1st International Symposium on Wireless Pervasive Computing.

[2]  Yu-Chee Tseng,et al.  The coverage problem in three-dimensional wireless sensor networks , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[3]  Jun-Hong Cui,et al.  DBR: Depth-Based Routing for Underwater Sensor Networks , 2008, Networking.

[4]  P. Lockhart,et al.  Introduction to Geometry , 1940, The Mathematical Gazette.

[5]  Zygmunt J. Haas,et al.  Coverage and connectivity in three-dimensional networks , 2006, MobiCom '06.

[6]  Krishnendu Chakrabarty,et al.  Sensor deployment and target localization based on virtual forces , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[7]  Mohamed K. Watfa.  Practical Applications and Connectivity Algorithms in Future Wireless Sensor Networks , 2008 .

[8]  Marco Zuniga,et al.  Analyzing the transitional region in low power wireless links , 2004, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004..

[9]  Miodrag Potkonjak,et al.  Exposure in Wireless Sensor Networks: Theory and Practical Solutions , 2002, Wirel. Networks.

[10]  Jun-Hong Cui,et al.  Scalable Localization with Mobility Prediction for Underwater Sensor Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[11]  Dong Xuan,et al.  On Deploying Wireless Sensors to Achieve Both Coverage and Connectivity , 2006, 2009 5th International Conference on Wireless Communications, Networking and Mobile Computing.

[12]  H. Davenport,et al.  The covering of space by spheres , 1952 .

[13]  Karl Sigmund,et al.  Kepler’s conjecture: How some of the greatest minds in history helped solve one of the oldest math problems in the world , 2004 .

[14]  T. Hales.  The Kepler conjecture , 1998, math/9811078.

[15]  Brian Neil Levine,et al.  A survey of practical issues in underwater networks , 2006, MOCO.

[16]  M. Bleicher.  Lattice Coverings of n-Space By Spheres , 1962, Canadian Journal of Mathematics.

[17]  Weijia Jia,et al.  Deploying Four-Connectivity and Full-Coverage Wireless Sensor Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[18]  Dario Pompili,et al.  Three-dimensional routing in underwater acoustic sensor networks , 2005, PE-WASUN '05.

[19]  George G. Szpiro,et al.  More on fisheries , 2003, Nature.

[20]  Wei Cheng,et al.  Underwater Localization in Sparse 3D Acoustic Sensor Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[21]  William Thomson.  On the division of space with minimum partitional area , 1887 .

[22]  R. Bambah,et al.  On lattice coverings by spheres , 1954 .

[23]  Tarek F. Abdelzaher,et al.  Analysis of Target Detection Performance for Wireless Sensor Networks , 2005, DCOSS.

[24]  Yuan Li,et al.  Research challenges and applications for underwater sensor networking , 2006, IEEE Wireless Communications and Networking Conference, 2006. WCNC 2006..

[25]  Weijia Jia,et al.  Complete optimal deployment patterns for full-coverage and k-connectivity (k≤6) wireless sensor networks , 2008, MobiHoc '08.

[26]  S. W. Thomson.  LXIII. On the division of space with minimum partitional area , 1887 .

[27]  R. P. Bambah.  Lattice coverings with four-dimensional spheres , 1954 .