Abstract
Connectivity, primarily a graph-theoretic concept, helps define the fault tolerance of wireless sensor networks (WSNs) in the sense that it enables the sensors to communicate with each other so their sensed data can reach the sink. On the other hand, sensing coverage, an intrinsic architectural feature of WSNs plays an important role in meeting application-specific requirements, for example, to reliably extract relevant data about a sensed field. Sensing coverage and network connectivity are not quite orthogonal concepts. In fact, it has been proven that connectivity strongly depends on coverage and hence considerable attention has been paid to establish tighter connection between them although only loose lower bound on network connectivity of WSNs is known. In this article, we investigate connectivity based on the degree of sensing coverage by studying k-covered WSNs, where every location in the field is simultaneously covered (or sensed) by at least k sensors (property known as k-coverage, where k is the degree of coverage). We observe that to derive network connectivity of k-covered WSNs, it is necessary to compute the sensor spatial density required to guarantee k-coverage. More precisely, we propose to use a model, called the Reuleaux Triangle, to characterize k-coverage with the help of Helly's Theorem and the analysis of the intersection of sensing disks of k sensors. Using a deterministic approach, we show that the sensor spatial density to guarantee k-coverage of a convex field is proportional to k and inversely proportional to the sensing range of the sensors. We also prove that network connectivity of k-covered WSNs is higher than their sensing coverage k. Furthermore, we propose a new measure of fault tolerance for k-covered WSNs, called conditional fault tolerance, based on the concepts of conditional connectivity and forbidden faulty sensor set that includes all the neighbors of a given sensor. We prove that k-covered WSNs can sustain a large number of sensor failures provided that the faulty sensor set does not include a forbidden faulty sensor set.
- Adlakha, S., and Srivastava, M. 2003. Critical density threshold for coverage in wireless sensor networks. In Proceedings of the IEEE Wireless Communication Networking Conference, 3, 1615--1620.Google Scholar
- Ai, J., and Abouzeid, A. 2006. Coverage by directional sensors in randomly deployed wireless sensor networks. J. Combinat. Optimiz. 11, 1, 21--41.Google ScholarCross Ref
- Ammari, H. M. and Das, S. K. 2008. Clustering-based minimum energy m-connected k-covered wireless sensor networks. TPC Best Paper Award, In Proceedings of the European Conference on Wireless Sensor Network, Lecture Notes in Computer Sciences, vol. 4913, 1--16. Google ScholarDigital Library
- Ammari, H. M. and Das, S. K. 2006. Coverage, connectivity, and fault tolerance measures of wireless sensor networks. In Proceedings of the International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), A. K. Datta and M. Gradinariu Eds., Lecture Notes in Computer Sciences, vol. 4280, 35--49. Google ScholarDigital Library
- Ammari, H. M. and Das, S. K. 2006. On computing conditional fault-tolerance measures for k-covered wireless sensor networks. In Proceedings of the 9th ACM/IEEE MSWim, 309--316. Google ScholarDigital Library
- Bai, X., Kumar, S., Xuan, D., Yun, Z. and Lai, T. H. 2006. Deploying wireless sensors to achieve both coverage and connectivity. In Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing, 131--142. Google ScholarDigital Library
- Balister, P. Bollobas, B., Sarkar, A. and Kumar, S. 2007. Reliable density estimates for achieving coverage and connectivity in thin strips of finite length. In Proceedings of the Annual International Conference on Mobile Computing and Networking, 75--86. Google ScholarDigital Library
- Bollobás, B. 2006. The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press.Google Scholar
- Bredin, J. L., Demaine, E. D., Hajiaghayi, M. and Rus, D. 2005. Deploying sensor networks with guaranteed capacity and fault-tolerance. In Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing, 309--319. Google ScholarDigital Library
- Cardei, M. and Wu, J. 2006. Energy-efficient coverage problems in wireless ad-hoc sensor networks. Comput. Comm. 29, 4, 413--420. Google ScholarDigital Library
- Chen, J., Kanj, I. and Wang, G. 2002. Hypercube network fault tolerance: A probabilistic approach. In Proceedings of the IEEE International Conference on Parallel Processing, 65--72. Google ScholarDigital Library
- Cortes, J., Martinez, S., Karatas, T. and Bullo, F. 2004. Coverage control for mobile sensing networks. IEEE Trans. Robot. Automat. 20, 2, 243--255.Google ScholarCross Ref
- Datta, A. K., Gradinariu, M., Linga, P. and Raipin-Parvedy, P. 2005. Self-* distributed query region covering in sensor networks. In Proceedings of the IEEE Symposium on Reliable Distributed Systems (SRDS). Google ScholarDigital Library
- Drougas, Y. and Kalogeraki, V. 2007. Distributed, reliable restoration techniques using wireless sensor devices. In Proceedings of the IEEE International Parallel and Distributed Processing Symposium, 1--10.Google Scholar
- Du, X. and Lin, F. 2005. Maintaining differentiated coverage in heterogeneous sensor networks. EURASIP J. Wirel. Comm. Netw. 5, 4, 565--572. Google ScholarDigital Library
- Esfahanian, A. 1989. Generalized measures of fault tolerance with application to n-cube networks. IEEE Trans. Comput. 38, 11, 1586--1591. Google ScholarDigital Library
- Esfahanian, A. and Hakimi, S. 1988. On computing a conditional edge-connectivity of a graph. Inform. Process. Lett. 27, 195--199. Google ScholarDigital Library
- Franceschetti, M., Cook, M. and Bruck, J. 2002. A geometric theorem for wireless network design optimization. Tech. rep. http://paradise.caltech.edu/papers/.Google Scholar
- Ghosh, A. and Das, S. K. 2006. Coverage and connectivity issues in wireless sensor networks. In Mobile, Wireless and Sensor Networks: Technology, Applications and Future Directions, R. Shorey, et al., Eds. Wiley-IEEE Press.Google Scholar
- Gupta, H., Zhou, Z., Das, S. R. and Gu, Q. 2006. Connected sensor cover: Self-organization of sensor networks for efficient query execution. IEEE/ACM Trans. Netw. 14, 1, 55--67. Google ScholarDigital Library
- Hall, P. 1988. Introduction to the Theory of Coverage Processes, John Wiley & Sons Inc., New York.Google Scholar
- Harary, F. 1983. Conditional connectivity. Netw. 13, 347--357.Google ScholarCross Ref
- Huang, C.-F. and Tseng, Y.-C. 2003. The coverage problem in a wireless sensor network. In Proceedings of the ACM International Workshop of Wireless Sensor Networks andj Applications, 115--121. Google ScholarDigital Library
- Kershner, R. 1939. The number of circles covering a set. Amer. J. Math. 61, 3, 665--671.Google ScholarCross Ref
- Kruskal, J. 1956. On the shortest spanning subtree of a graph and the traveling salesman problem. In Amer. Math. Soc. 7, 48--50.Google ScholarCross Ref
- Kumar, S., Lai, T. H. and Arora, A. 2005. Barrier coverage with wireless sensors. In Proceedings of the ACM Annual International Conference on Mobile Computing and Networking, 284--298. Google ScholarDigital Library
- Kumar, S., Lai, T. H. and Balogh, J. 2004. On k-coverage in a mostly sleeping sensor network. In Proceedings of the ACM Annual International Conference on Mobile Computing and Networking, 144--158. Google ScholarDigital Library
- Latifi, S., Hegde, M. and Naraghi-Pour, M. 1994. Conditional connectivity measures for large multiprocessor systems. IEEE Trans. Comput. 43, 2, 218--222. Google ScholarDigital Library
- Lazos, L. and Poovendran, R. 2006. Coverage in heterogeneous sensor networks. In Proceedings of the Workshop on Modeling Optimization in Mobile, Ad Hoc and Sensor Systems, 1--10.Google Scholar
- Li, N. and Hou, J. 2004. FLSS: A fault-tolerant topology control algorithm for wireless networks. In Proceedings of the ACM Annual International Conference on Mobile Computing and Networking, 275--286. Google ScholarDigital Library
- Li, X.-Y. Wan, P.-J. and Frieder, O. 2003. Coverage in wireless ad-hoc sensor networks. IEEE Trans. Comput. 52, 753--763. Google ScholarDigital Library
- Luo, J. and Hubaux, J.-P. 2005. Joint mobility and routing for lifetime elongation in wireless sensor networks. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communication Societies, 1735--1746.Google Scholar
- Malde, P. and Oellermann, O. 1988. The F-connectivity of a graph. Scientia, Series A: Mathematical Sciences, 1, 65--71.Google Scholar
- Megerian, S., Koushanfar, F., Potkonjak, M. and Srivastava, M. 2005. Worst and best-case coverage in sensor networks. IEEE Trans. Mobile Comput. 4, 1, 84--92. Google ScholarDigital Library
- Megerian, S., Koushanfar, F., Potkonjak, M. and Srivastava, M. 2001. Coverage problems in wireless ad-hoc sensor networks. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communication Societies, 1380--1387.Google Scholar
- Oellermann, O. 1991. Conditional graph connectivity relative to hereditary properties. Netw. 21, 245--255.Google ScholarCross Ref
- Ravelomanana, V. 2004. Extremal properties of three-dimensional sensor networks with applications. IEEE Trans. Mobile Comput. 3, 3, 246--257. Google ScholarDigital Library
- Shakkottai, S., Srikant, R. and Shroff, N. 2005. Unreliable sensor grids: coverage, connectivity and diameter. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communication Societies, 1073--1083.Google Scholar
- Tian, D. and Georganas, N. 2005. Connectivity maintenance and coverage preservation in wireless sensor networks. Ad Hoc Netw. 3, 744--761. Google ScholarDigital Library
- Wan, P.-J. and Yi, C.-W. 2006. Coverage by randomly deployed wireless sensor networks. IEEE/ACM Trans. Netw. 14, 2658--2669. Google ScholarDigital Library
- Wang, X., Xing, G., Zhang, Y., Lu, C., Pless, R. and Gill, C. 2003. Integrated coverage and connectivity configuration in wireless sensor networks. In Proceedings of the ACM Conference on Embedded Network Sensor Systems, 28--39. Google ScholarDigital Library
- Wu, J. and Guo, G. 1998. Fault tolerance measures for m-ary n-dimensional hypercubes based on forbidden faulty sets. IEEE Trans. Comput. 47, 8, 888--893. Google ScholarDigital Library
- Xing, G., Wang, X., Zhang, Y., Lu, C., Pless, R. and Gill, C. 2005. Integrated coverage and connectivity configuration for energy conservation in sensor networks. ACM Trans. Sens. Netw. 1, 1, 36--72. Google ScholarDigital Library
- Yarvis, M., Kushalnagar, N., Singh, H., Rangarajan, A., Liu, Y., and Singh, S. 2005. Exploiting heterogeneity in sensor networks. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communication Societies, 878--890.Google Scholar
- Zhang, H. and Hou, J. 2006. Is deterministic deployment worse than random deployment for wireless sensor networks? In Proceedings of the Annual Joint Conference of the IEEE Computer and Communication Societies, 1--13.Google Scholar
- Zhang, H. and Hou, J. 2005. On the upper bound of α-lifetime for large sensor networks. ACM Trans. Sensor Netw. 1, 2, 272--300. Google ScholarDigital Library
- Zhang, H. and Hou, J. 2005. Maintaining sensing coverage and connectivity in large sensor networks. Ad Hoc Sensor Wirel. Netw. 1, 1--2, 89--124.Google Scholar
- Zhang, H. and Hou, J. 2004. On deriving the upper bound of α -lifetime for large sensor networks. In Proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing, 121--132. Google ScholarDigital Library
- Zhao, J. and Govindan, R. 2003. Understanding packet delivery performance in dense wireless sensor networks. In Proceedings of the ACM Conference on Embedded Network Sensor Systems, 1--13. Google ScholarDigital Library
- Zhou, Z., Das, S. and Gupta, H. 2005. Fault tolerant connected sensor cover with variable sensing and transmission ranges. In Proceedings of the IEEE International Conference on Sensor and Ad Hoc Communications and Networks, 594--604.Google Scholar
- Zhou, G., He, T., Krishnamurthy, S. and Stankovic, J. 2004. Impact of radio irregularity on wireless sensor networks. In Proceedings of the MobiSys, 125--138. Google ScholarDigital Library
Index Terms
- Fault tolerance measures for large-scale wireless sensor networks
Recommendations
Joint k-coverage and data gathering in sparsely deployed sensor networks -- Impact of purposeful mobility and heterogeneity
Coverage is one of the fundamental concepts in the design of wireless sensor networks (WSNs) in the sense that the monitoring quality of a phenomenon depends on the quality of service provided by the sensors in terms of how well a field of interest is ...
Coverage, connectivity, and fault tolerance measures of wireless sensor networks
SSS'06: Proceedings of the 8th international conference on Stabilization, safety, and security of distributed systemsConnectivity and sensing coverage are two fundamental concepts in the design of wireless sensor networks (WSNs). In this paper, we investigate the relationship between coverage and connectivity for k-covered WSNs (kCWSN), where every point in a field of ...
Connectivity preserving localized coverage algorithm for area monitoring using wireless sensor networks
Efficient network coverage and connectivity are the requisites for most Wireless Sensor Network (WSN) deployments, particularly those concerned with area monitoring. Due to the resource constraints of the sensor nodes, redundancy of coverage area must ...
Comments