Efficient deployment of connected sensing devices using circle packing algorithms

In this paper, we explore different sensor deployment problems and how these problems can be solved optimally using the current packing approaches in terms of small-scale problems. In addition, we consider the deployment of either homogenous or heterogeneous sensing devices. The deployment objectives are to maximize the coverage of the monitored field and use the best of the sensing devices characteristics as well as developing a connected deployment scheme. We propose a novel algorithm named Sequential Packing-based Deployment Algorithm (SPDA) for the deployment of heterogeneous sensors in order to maximize the coverage of the monitored field and connectivity of the deployed sensors. The algorithm is inspired from the packing theories in computational geometry where it benefits from many of the observations properties that are captured from the optimal packing solutions. The algorithm efficiency is examined using different case studies.

[1]  Gaurav S. Sukhatme,et al.  An Incremental Self-Deployment Algorithm for Mobile Sensor Networks , 2002, Auton. Robots.

[2]  Ruchu Xu,et al.  Local Search Based on a Physical Model for Solving a Circle Packing Problem , 2001 .

[3]  Yunhui Liu,et al.  Heterogeneous Sensor Network Deployment Using Circle Packings , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[4]  ScienceDirect Computational geometry : theory and applications. , 1991 .

[5]  Bernardetta Addis,et al.  Disk Packing in a Square: A New Global Optimization Approach , 2008, INFORMS J. Comput..

[6]  Gaurav S. Sukhatme,et al.  Autonomous deployment and repair of a sensor network using an unmanned aerial vehicle , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[7]  Jennifer C. Hou,et al.  Maintaining Sensing Coverage and Connectivity in Large Sensor Networks , 2005, Ad Hoc Sens. Wirel. Networks.

[8]  Tomasz Dubejko,et al.  Recurrent random walks, Liouville's theorem and circle packings , 1995, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  Yunhui Liu,et al.  Sensor Network Deployment Using Circle Packings , 2008, ICOIN.

[10]  Computer-Assisted Intervention,et al.  Medical Image Computing and Computer-Assisted Intervention – MICCAI’99 , 1999, Lecture Notes in Computer Science.

[11]  Kenneth Stephenson,et al.  Introduction to Circle Packing: The Theory of Discrete Analytic Functions , 2005 .

[12]  Guoliang Xing,et al.  Integrated coverage and connectivity configuration for energy conservation in sensor networks , 2005, TOSN.

[13]  J. Schaer The Densest Packing of 9 Circles in a Square , 1965, Canadian Mathematical Bulletin.

[14]  David Dennis,et al.  Layered circle packings , 2005, Int. J. Math. Math. Sci..

[15]  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.

[16]  Kenneth Stephenson,et al.  A circle packing algorithm , 2003, Comput. Geom..

[17]  Y. Li,et al.  Greedy algorithms for packing unequal circles into a rectangular container , 2005, J. Oper. Res. Soc..

[18]  GillChristopher,et al.  Integrated coverage and connectivity configuration for energy conservation in sensor networks , 2005 .

[19]  A. Repp Discrete Riemann Maps and the Parabolicity of Tilings , 1998 .

[20]  David A. Rottenberg,et al.  Quasi-Conformally Flat Mapping the Human Cerebellum , 1999, MICCAI.

[21]  V. Chvátal A combinatorial theorem in plane geometry , 1975 .

[22]  Gaurav S. Sukhatme,et al.  Deployment and Connectivity Repair of a Sensor Net with a Flying Robot , 2004, ISER.

[23]  K. Nurmela,et al.  COVERING A SQUARE WITH UP TO 30 EQUAL CIRCLES , 2000 .

[24]  Kenneth Stephenson Circle Packing : A Mathematical Tale , 2003 .

[25]  Defu Zhang,et al.  Packing Different-sized Circles into a Rectangular Container Using Simulated Annealing Algorithm , 2004, International Conference on Computational Intelligence.

[26]  H. Melissen,et al.  Densest Packing of Six Equal Circles in a Square. , 1994 .