Abstract
In wireless sensor networks (WSNs), a space filling curve (SFC) refers to a path passing through all nodes in the network, with each node visited at least once. By enforcing a linear order of the sensor nodes through an SFC, many applications in WSNs concerning serial operations on both sensor nodes and sensor data can be performed, with examples including serial data fusion and path planning of mobile nodes. Although a few studies have made efforts to find such SFCs in WSNs, they primarily target 2D planar or 3D surface settings and cannot be directly applied to 3D volumetric WSNs due to considerably more complex geometric features and topology shapes that the 3D volumetric settings introduce. This article presents BLOW-UP, a distributed, scalable, and connectivity-based algorithm to construct an SFC for a 3D volumetric WSN (or alternatively to linearize the 3D volumetric network). The main idea of BLOW-UP is to decompose the given 3D volumetric network into a series of connected and closed layers, and the nodes are traversed layer by layer, incrementally from the innermost to the outermost, yielding an SFC covering the entire network, provably at least once and at most a constant number of times. To the best of our knowledge, BLOW-UP is the first algorithm that realizes linearization in 3D volumetric WSNs. It does not require advance knowledge of location or distance information. It is also scalable with a nearly constant per-node storage cost and message cost. Extensive simulations under various networks demonstrate its effectiveness on nodes’ covered times, coverage rate, and covering speed.
- M. Ahmed and S. Bokhari. 2007. Mapping with space filling surfaces. IEEE Transactions on Parallel and Distributed Systems 18, 9, 1258--1269. Google ScholarDigital Library
- I. F. Akyildiz and M. C. Vuran. 2010. Wireless Sensor Networks. John Wiley & Sons. Google ScholarDigital Library
- M. Bader. 2012. Space-Filling Curves: An Introduction with Applications in Scientific Computing. Texts in Computational Science and Engineering, Vol. 9. Springer. Google ScholarDigital Library
- J. M. Bahi, A. Makhoul, and A. Mostefaoui. 2008. Hilbert mobile beacon for localisation and coverage in sensor networks. International Journal of Systems Science 39, 11, 1081--1094. Google ScholarDigital Library
- X. Ban, M. Goswami, W. Zeng, X. Gu, and J. Gao. 2013. Topology dependent space filling curves for sensor networks and applications. In Proceedings of the IEEE INFOCOM Conference (INFOCOM’13). 2166--2174.Google Scholar
- R. S. Blum, S. A. Kassam, and H. V. Poor. 1997. Distributed detection with multiple sensors II. Advanced topics. Proceedings of the IEEE 85, 1, 64--79.Google ScholarCross Ref
- F. Cadger, K. Curran, J. Santos, and S. Moffett. 2013. A survey of geographical routing in wireless ad-hoc networks. IEEE Communications Surveys and Tutorials 15, 2, 621--653.Google ScholarCross Ref
- J. Flich, T. Skeie, A. Mejia, O. Lysne, P. Lopez, A. Robles, J. Duato, M. Koibuchi, T. Rokicki, and J. C. Sancho. 2012. A survey and evaluation of topology-agnostic deterministic routing algorithms. IEEE Transactions on Parallel and Distributed Systems 23, 3, 405--425. Google ScholarDigital Library
- J. Gao and L. Zhang. 2006. Load-balanced short-path routing in wireless networks. IEEE Transactions on Parallel and Distributed Systems 17, 4, 377--388. Google ScholarDigital Library
- M. R. Garey, D. S. Johnson, and R. E. Tarjan. 1976. The planar Hamiltonian circuit problem is NP-complete. SIAM Journal on Computing 5, 4, 704--714.Google ScholarDigital Library
- C. Gold. 1999. Crust and anti-crust: A one-step boundary and skeleton extraction algorithm. In Proceedings of ACM Symposium on Computational Geometry. 189--196. Google ScholarDigital Library
- C. Gold and J. Snoeyink. 2001. A one-step crust and skeleton extraction algorithm. Algorithmica 30, 2, 144--163. Google ScholarDigital Library
- D. Hilbert. 1891. Ueber die stetige abbildung einer line auf ein fachenstuck. Mathematische Annalen 38, 3, 459--460.Google ScholarCross Ref
- H. Jiang, T. Yu, C. Tian, G. Tan, and C. Wang. 2015. Connectivity-based segmentation in large-scale 2-D/3-D sensor networks: Algorithm and applications. IEEE/ACM Transactions on Networking 23, 1, 15--27. Google ScholarDigital Library
- D. B. Johnson and D. A. Maltz. 1996. Dynamic source routing in ad hoc wireless networks. In Mobile Computing. Kluwer International Series in Engineering and Computer Science, Vol. 353. Kluwer, 153--181.Google Scholar
- M. Kamat, A. S. Ismail, and S. Olariu. 2007. Modified Hilbert space-filling curve for ellipsoidal coverage in wireless ad hoc sensor networks. In Proceedings of the IEEE ICSPC Conference (ICSPC’07). 1407--1410.Google Scholar
- S. Kar, J. M. F. Moura, and K. Ramanan. 2012. Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication. IEEE Transactions on Information Theory 58, 6, 3575--3605. Google ScholarDigital Library
- D. Koutsonikolas, S. M Das, and Y. C. Hu. 2007. Path planning of mobile landmarks for localization in wireless sensor networks. Computer Communications 30, 13, 2577--2592. Google ScholarDigital Library
- F. Kuhn, R. Wattenhofer, and A. Zollinger. 2003. Worst-case optimal and average-case efficient geometric ad-hoc routing. In Proceedings of the ACM MobiHoc Conference (MobiHoc’03). 267--278. Google ScholarDigital Library
- F. Li, C. Zhang, J. Luo, S. Xin, and Y. He. 2014. LBDP: Localized boundary detection and parametrization for 3-D sensor networks. IEEE/ACM Transactions on Networking 22, 2, 567--579. Google ScholarDigital Library
- W. Liang, P. Schweitzer, and Z. Xu. 2013. Approximation algorithms for capacitated minimum forest problems in wireless sensor networks with a mobile sink. IEEE Transactions on Computers 62, 10, 1932--1944. Google ScholarDigital Library
- Y. Luo, L. Pu, M. Zuba, Z. Peng, and J.-H. Cui. 2014. Challenges and opportunities of underwater cognitive acoustic networks. IEEE Transactions on Emerging Topics in Computing 2, 2, 109--211.Google ScholarCross Ref
- A. Madhja, S. Nikoletseas, and T. P. Raptis. 2015. Distributed wireless power transfer in sensor networks with multiple mobile chargers. Computer Networks 80, 7, 89--108. Google ScholarDigital Library
- E. Masazade, R. Niu, P. K. Varshney, and M. Keskinoz. 2010. Energy aware iterative source localization for wireless sensor networks. IEEE Transactions on Signal Processing 58, 9, 4824--4835. Google ScholarDigital Library
- A. Mostefaoui, A. Boukerche, M. A. Merzoug, and M. Melkemi. 2015. A scalable approach for serial data fusion in wireless sensor networks. Computer Networks 79, 14, 103--119. Google ScholarDigital Library
- A. Nedic, A. Olshevsky, A. Ozdaglar, and J. N. Tsitsiklis. 2009. On distributed averaging algorithms and quantization effects. IEEE Transactions on Automatic Control 54, 11, 2506--2517.Google ScholarCross Ref
- Y. Noh, U. Lee, P. Wang, B. S. C. Choi, and M. Gerla. 2013. VAPR: Void-aware pressure routing for underwater sensor networks. IEEE Transactions on Mobile Computing 12, 5, 895--908. Google ScholarDigital Library
- S. Patil, S. R. Das, and A. Nasipuri. 2004. Serial data fusion using space-filling curves in wireless sensor networks. In Proceedings of the IEEE SECON Conference (SECON’04). 182--190.Google Scholar
- G. Peano. 1890. Sur une courbe, qui remplit toute une aire plane. Mathematische Annalen 36, 1, 157--160.Google ScholarCross Ref
- C. Perera, A. Zaslavsky, C. H. Liu, M. Compton, P. Christen, and D. Georgakopoulos. 2014. Sensor search techniques for sensing as a service architecture for the Internet of Things. IEEE Sensors Journal 14, 2, 406--420.Google ScholarCross Ref
- T. L. Porta, C. Petrioli, C. Phillips, and D. Spenza. 2014. Sensor mission assignment in rechargeable wireless sensor networks. ACM Transactions on Sensor Networks 10, 4, 60:1--60:39. Google ScholarDigital Library
- R. Rajagopalan and P. K. Varshney. 2006. Data aggregation techniques in sensor networks: A survey. IEEE Communications Surveys and Tutorials 8, 4, 48--63. Google ScholarDigital Library
- H. Sagan. 1994. Space-Filling Curves. Springer-Verlag, New York, NY.Google Scholar
- R. C. Shah, S. Roy, S. Jain, and W. Brunette. 2003. Data mules: Modeling and analysis of a three-tier architecture for sparse sensor networks. Ad Hoc Networks 1, 2, 215--233.Google ScholarCross Ref
- F. Spitzer. 2001. Principles of Random Walk. Vol. 34. Springer.Google Scholar
- R. Sugihara and R. K. Gupta. 2011. Path planning of data mules in sensor networks. ACM Transactions on Sensor Networks 8, 1, 1:1--1:27. Google ScholarDigital Library
- G. Tan, H. Jiang, J. Liu, and A.-M. Kermarrec. 2014. Convex partitioning of large-scale sensor networks in complex fields: Algorithms and applications. ACM Transactions on Sensor Networks 10, 3, 41:1--41:23. Google ScholarDigital Library
- G. Tan, H. Jiang, S. Zhang, Z. Yin, and A.-M. Kermarrec. 2013. Connectivity-based and anchor-free localization in large-scale 2D/3D sensor networks. ACM Transactions on Sensor Networks 10, 1, 6:1--6:21. Google ScholarDigital Library
- R. Tan, G. Xing, J. Wang, and B. Liu. 2011. Performance analysis of real-time detection in fusion-based sensor networks. IEEE Transactions on Parallel and Distributed Systems 22, 9, 1564--1577. Google ScholarDigital Library
- O. Tekdas, V. Isler, L. J. Hyun, and A. Terzis. 2009. Using mobile robots to harvest data from sensor fields. IEEE Wireless Communications 16, 1, 22--28. Google ScholarDigital Library
- C. Tunca, S. Isik, M. Y. Donmez, and C. Ersoy. 2014. Distributed mobile sink routing for wireless sensor networks: A survey. IEEE Communications Surveys and Tutorials 16, 2, 877--897.Google ScholarCross Ref
- R. Viswanathan and P. K. Varshney. 1997. Distributed detection with multiple sensors I. Fundamentals. Proceedings of the IEEE 85, 1, 54--63.Google ScholarCross Ref
- C. Wang and H. Jiang. 2015. SURF: A connectivity-based space filling curve construction algorithm in high genus 3D surface WSNs. In Proceedings of the IEEE INFOCOM Conference (INFOCOM’15). 981--989.Google Scholar
- C. Wang, H. Ma, Y. He, and S. Xiong. 2012. Adaptive approximate data collection for wireless sensor networks. IEEE Transactions on Parallel and Distributed Systems 23, 6, 1004--1016. Google ScholarDigital Library
- S. Xia, H. Wu, and M. Jin. 2014. Trace-routing in 3D wireless sensor networks: A deterministic approach with constant overhead. In Proceedings of the ACM MobiHoc Conference (MobiHoc’14). 357--366. Google ScholarDigital Library
- S. Xia, X. Yin, H. Wu, M. Jin, and X. D. Gu. 2011. Deterministic greedy routing with guaranteed delivery in 3D wireless sensor networks. In Proceedings of the ACM MobiHoc Conference (MobiHoc’11). 1--10. Google ScholarDigital Library
- L. Xie, Y. Shi, Y. T. Hou, and H. D. Sherali. 2012. Making sensor networks immortal: An energy-renewal approach with wireless power transfer. IEEE/ACM Transactions on Networking 20, 6, 1748--1761. Google ScholarDigital Library
- K. Yang. 2014. Wireless Sensor Networks. Springer.Google Scholar
- F. Ye, H. Luo, J. Cheng, S. Lu, and L. Zhang. 2002. A two-tier data dissemination model for large-scale wireless sensor networks. In Proceedings of the ACM MobiCom Conference (MobiCom’02). 148--159. Google ScholarDigital Library
- H. Zhang and H. Shen. 2009. Balancing energy consumption to maximize network lifetime in data-gathering sensor networks. IEEE Transactions on Parallel and Distributed Systems 20, 10, 1526--1539. Google ScholarDigital Library
- H. Zhou, N. Ding, M. Jin, S. Xia, and H. Wu. 2011. Distributed algorithms for bottleneck identification and segmentation in 3D wireless sensor networks. In Proceedings of the IEEE SECON Conference (SECON’11). 494--502.Google Scholar
- M. Zhu, S. Ding, Q. Wu, R. R. Brooks, N. S. V. Rao, and S. S. Iyengar. 2010. Fusion of threshold rules for target detection in wireless sensor networks. ACM Transactions on Sensor Networks 6, 2, 18:1--18:7. Google ScholarDigital Library
Index Terms
- BLOW-UP: Toward Distributed and Scalable Space Filling Curve Construction in 3D Volumetric WSNs
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