Approximation Algorithm for Line Segment Coverage for Wireless Sensor Network

The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments in sensor networks. A line segment l is said to be covered if it intersects the sensing regions of at least one sensor distributed in that region. We show that the problem of finding the minimum number of sensors needed to cover each member in a given set of line segments in a rectangular area is NP-hard. Next, we propose a constant factor approximation algorithm for the problem of covering a set of axis-parallel line segments. We also show that a PTAS exists for this problem.

[1]  Yu-Chee Tseng,et al.  The Coverage Problem in a Wireless Sensor Network , 2003, WSNA '03.

[2]  Xiaohua Jia,et al.  Coverage problems in wireless sensor networks: designs and analysis , 2008, Int. J. Sens. Networks.

[3]  Alessandro Agnetis,et al.  Covering a line segment with variable radius discs , 2007, Comput. Oper. Res..

[4]  Xiaojiang Du,et al.  Improving coverage performance in sensor networks by using mobile sensors , 2005, MILCOM 2005 - 2005 IEEE Military Communications Conference.

[5]  Miodrag Potkonjak,et al.  Worst and best-case coverage in sensor networks , 2005, IEEE Transactions on Mobile Computing.

[6]  Silvia Ferrari,et al.  A Geometric Transversal Approach to Analyzing Track Coverage in Sensor Networks , 2008, IEEE Transactions on Computers.

[7]  Parameswaran Ramanathan,et al.  Sensor deployment strategy for target detection , 2002, WSNA '02.

[8]  Yeh-Ching Chung,et al.  A Delaunay triangulation based method for wireless sensor network deployment , 2006, 12th International Conference on Parallel and Distributed Systems - (ICPADS'06).

[9]  Bin Ma,et al.  Sensor networks deployment using flip-based sensors , 2005, IEEE International Conference on Mobile Adhoc and Sensor Systems Conference, 2005..

[10]  Thomas F. La Porta,et al.  Bidding Protocols for Deploying Mobile Sensors , 2007, IEEE Transactions on Mobile Computing.

[11]  Xiangke Liao,et al.  Barrier Coverage with Mobile Sensors , 2008, 2008 International Symposium on Parallel Architectures, Algorithms, and Networks (i-span 2008).

[12]  Luérbio Faria,et al.  On minimum clique partition and maximum independent set on unit disk graphs and penny graphs: complexity and approximation , 2004, Electron. Notes Discret. Math..

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

[14]  Anish Arora,et al.  Barrier coverage with wireless sensors , 2005, MobiCom '05.

[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]  C. Siva Ram Murthy,et al.  Dynamic Coverage Maintenance Algorithms for Sensor Networks with Limited Mobility , 2005, Third IEEE International Conference on Pervasive Computing and Communications.

[17]  Ioannis G. Tollis,et al.  Planar grid embedding in linear time , 1989 .

[19]  Timothy M. Chan,et al.  Approximating the piercing number for unit-height rectangles , 2005, CCCG.