Cited By
View all- Huang CKo R(2015)A Study on Maximizing the Parallelism of Macroscopically Derived Routing Algorithms for WSNsThe Computer Journal10.1093/comjnl/bxv03658:12(3306-3324)Online publication date: 30-May-2015
Gauss-seidel correction algorithm: A macroscopic model-derived routing algorithm for WSNs
Article No.: 9, Pages 1 - 42
Abstract
A Gauss-Seidel correction (GSC) routing algorithm for wireless sensor networks is presented in which packets are transmitted with additional information which can be exchanged among nodes to correct the current routing paths and achieve load balancing. The problem considered here is single-class routing to one/multiple sinks with lifetime maximization as the objective. The formulation to correct the routing paths is not heuristic and takes its theoretical basis from a macroscopic model, that is, based on a set of partial differential equations iteratively solved by the Gauss-Seidel method. We then theoretically investigate the convergence of GSC. Furthermore, an initial value estimation algorithm is presented to alleviate the long-path problem during the delivery of the first several packets, thus accelerating the convergence of GSC. Simulation results show that GSC effectively achieves load balancing, particularly for regions of interest with holes.
References
[1]
Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., and Cayirci, E. E. 2002. A survey on sensor networks. IEEE Commun. Mag. 40, 8, 102--114.
[2]
Altman, E., Bernhard, P., and Silva, A. 2008. The mathematics of routing in massively dense ad-hoc networks. In Proceedings of the 7th International Conference on Ad-Hoc, Mobile and Wireless Networks. Springer-Verlag, 122--134.
[3]
Babuska, I. 1961. On randomised solutions of Laplace's equation. Časopis pro pěstování matematiky 86, 3, 269--276.
[4]
Bécus, G. A. and Cozzarelli, F. A. 1976a. The random steady state diffusion problem I: Random generalized solutions to Laplace's equation. SIAM J. Appl. Math. 31, 1, 134--147.
[5]
Bécus, G. A. and Cozzarelli, F. A. 1976b. The random steady state diffusion problem II: Random solutions to nonlinear, inhomogeneous, steady state diffusion problems. SIAM J. Appl. Math. 31, 1, 148--158.
[6]
Bécus, G. A. and Cozzarelli, F. A. 1976c. The random steady state diffusion problem III: Solutions to random diffusion problems by the method of random successive approximations. SIAM J. Appl. Math. 31, 1, 159--178.
[7]
Björck, Å. and Elfving, T. 1979. Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations. BIT Numeri. Math. 19, 2, 145--163.
[8]
Catanuto, R., Morabito, G., and Toumpis, S. 2006. Optical routing in massively dense networks: Practical issues and dynamic programming interpretation. In Proceedings of the 3rd International Symposium on Wireless Communications Systems.
[9]
Catanuto, R., Toumpis, S., and Morabito, G. 2007. Opti{c, m}al: Optical/optimal routing in massively dense wireless networks. In Proceeding of the 26th Annual IEEE Conference on Computer Communications (INFOCOM'07). 1010--1018.
[10]
Catanuto, R., Toumpis, S., and Morabito, G. 2009. On asymptotically optimal routing in large wireless networks and geometrical optics analogy. Comput. Netw. 53, 11, 1939--1955.
[11]
Chiasserini, C.-F., Gaeta, R., Garetto, M., Gribaudo, M., Manini, D., and Sereno, M. 2007. Fluid models for large-scale wireless sensor networks. Perform. Eval. 64, 7--8, 715--736.
[12]
Finn, G. G. 1987. Routing and addressing problems in large metropolitan-scale internetworks. Res. Tech. rep. ISI/RR-87-180, Information Sciences Institute.
[13]
Gabriel, R. K. and Sokal, R. R. 1969. A new statistical approach to geographic variation analysis. System. Zoology 18, 3, 259--278.
[14]
Golub, G. H. and van Loan, C. F. 1996. Matrix Computations 3rd Ed. The Johns Hopkins University Press, Baltimore, MD.
[15]
Gupta, P. and Kumar, P. R. 2000. The capacity of wireless networks. IEEE Trans. Inform. Theory 46, 2, 388--404.
[16]
Hackbusch, W. 1994. Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol. 95, Springer-Verlag, Berling.
[17]
Haghpanahi, M., Kalantari, M., and Shayman, M. 2009. Implementing information paths in a dense wireless sensor network. In Proceedings of the 28th IEEE Conference on Global Telecommunications. IEEE Press, 5412--5418.
[18]
Heinzelman, W. R., Chandrakasan, A., and Balakrishnan, H. 2000. Energy-efficient communication protocol for wireless microsensor networks. In Proceedings of the 33rd Hawaii International Conference on System Sciences. Vol. 8. IEEE Computer Society.
[19]
Hyytiä, E. and Virtamo, J. 2007a. On optimality of single-path routes in massively dense wireless multi-hop networks. In Proceedings of the 10th ACM Symposium on Modeling, Analysis, and Simulation of Wireless and Mobile Systems. ACM, 28--35.
[20]
Hyytiä E. and Virtamo, J. 2007b. On traffic load distribution and load balancing in dense wireless multihop networks. EURASIP J. Wirel. Commun. Netw. 2007, 1, 21.
[21]
Hyytiä, E. and Virtamo, J. 2009. On the optimality of field-line routing in massively dense wireless multi-hop networks. Perform. Eval. 66, 3-5, 158--172.
[22]
Jacquet, P. 2004. Geometry of information propagation in massively dense ad hoc networks. In Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing. 157--162.
[23]
Jung, S., Kserawi, M., Lee, D., and Rhee, J.-K. K. 2009. Distributed potential field based routing and autonomous load balancing for wireless mesh networks. IEEE Commun. Lett. 13, 6, 429--431.
[24]
Kalantari, M. and Shayman, M. 2004. Energy efficient routing in wireless sensor networks. In Proceedings of the Conference on Information Sciences and Systems.
[25]
Kalantari, M. and Shayman, M. 2006a. Design optimization of multi-sink sensor networks by analogy to electrostatic theory. In Proceedings of the IEEE Wireless Communications and Networking Conference. 431--438.
[26]
Kalantari, M. and Shayman, M. 2006b. Routing in multi-commodity sensor networks based on partial differential equations. In Proceedings of the 40th Annual Conference on Information Sciences and Systems. 402--406.
[27]
Karp, B. and Kung, H. T. 2000. GPSR: Greedy perimeter stateless routing for wireless networks. In Proceedings of the 6th Annual International Conference on Mobile Computing and Networking. ACM, 243--254.
[28]
Ko, R.-S. 2013. Analyzing the redeployment problem of mobile wireless sensor networks via geographic models. Wirel. Commun. Mobile Comput. 13, 2, 111--129.
[29]
Ko, R.-S. 2011a. A distributed routing algorithm for sensor networks derived from macroscopic models. Comput. Netw. 55, 1, 314--329.
[30]
Ko, R.-S. 2011b. Macroscopic analysis of wireless sensor network routing problems. Adhoc Sen. Wirel. Netw. 13, 1--2, 59--85.
[31]
Marsden, J. E. and Tromba, A. J. 2003. Vector Calculus 5th Ed. W. H. Freeman.
[32]
Royer, E. M. and Toh, C.-K. 1999. A review of current routing protocols for ad hoc mobile wireless networks. IEEE Personal Commun. Mag. 6, 46--55.
[33]
Silva, A., Altman, E., and Bernhard, P. 2008. Numerical solutions of continuum equilibria for routing in dense ad-hoc networks. In Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools. Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering.
[34]
Silva, A., Altman, E., Bernhard, P., and Debbah, M. 2010a. Continuum equilibria and global optimization for routing in dense static ad-hoc networks. Comput. Netw. 54, 6, 1005--1018.
[35]
Silva, A., Altman, E., Debbah, M., and Alfano, G. 2010b. Magnetworks: How mobility impacts the design of mobile ad hoc networks. In Proceedings of the 29th Annual IEEE Conference on Computer Communications (INFOCOM'10). IEEE Press, 1729--1737.
[36]
Toumpis, S. 2006. Optimal design and operation of massively dense wireless networks: how to solve 21st century problems using 19th century mathematics. In Proceedings of the Workshop on Interdisciplinary Systems Approach in Performance Evaluation and Design of Computer & Communications Systems. ACM Press.
[37]
Toumpis, S. 2008. Mother nature knows best: A survey of recent results on wireless networks based on analogies with physics. Comput. Netw. 52, 2, 360--383.
[38]
Toussaint, G. T. 1980. The relative neighbourhood graph of a finite planar set. Pattern Recog. 12, 4, 261--268.
[39]
Yu, Y., Govindan, R., and Estrin, D. 2001. Geographical and energy aware routing: A recursive data dissemination protocol for wireless sensor networks. Tech. rep. UCLA/CSD-TR-01-0023, Computer Science Department, UCLA. May.
[40]
Zhao, F. and Guibas, L. 2004. Wireless Sensor Networks: An Information Processing Approach. Morgan Kaufmann Publishers Inc., San Francisco, CA.
Index Terms
- Gauss-seidel correction algorithm: A macroscopic model-derived routing algorithm for WSNs
Recommendations
Distributed De La Garza algorithm for load-balancing routing in wireless sensor networks
Large scale wireless sensor networks raise many challenges in the design of efficient and effective routing algorithm due to their complexity and hardware constraints. However, the scalability challenge may be mitigated from a macroscopic perspective. ...
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
We give new convergence results for the block Gauss-Seidel method for problems where the feasible set is the Cartesian product of m closed convex sets, under the assumption that the sequence generated by the method has limit points. We show that the ...
Supervisory routing control for dynamic load balancing in low data rate wireless sensor networks
Routing protocols for Wireless Sensor Networks (WSN) are designed to select parent nodes so that data packets can reach their destination in a timely and efficient manner. Typically neighboring nodes with strongest connectivity are more selected as ...
Comments
Information & Contributors
Information
Published In
Copyright © 2013 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Publisher
Association for Computing Machinery
New York, NY, United States
Journal Family
Publication History
Published: 06 December 2013
Accepted: 01 February 2013
Revised: 01 May 2012
Received: 01 February 2012
Published in TOSN Volume 10, Issue 1
Check for updates
Author Tags
Qualifiers
- Research-article
- Research
- Refereed
Funding Sources
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 189Total Downloads
- Downloads (Last 12 months)4
- Downloads (Last 6 weeks)0
Reflects downloads up to 22 Sep 2024
Other Metrics
Citations
Cited By
View all- Huang CKo R(2015)A Study on Maximizing the Parallelism of Macroscopically Derived Routing Algorithms for WSNsThe Computer Journal10.1093/comjnl/bxv03658:12(3306-3324)Online publication date: 30-May-2015
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in