# The Complexity of Data Aggregation in Static and Dynamic Wireless Sensor Networks

## Abstract

The key feature of wireless sensor networks is to aggregate data collected by individual sensors in an energy efficient manner. We consider two techniques to save energy. The first one is to avoid collisions due to simultaneous transmissions among neighboring nodes. Second, when a node receives data from multiple neighbors, it aggregates these with its own data. Then, one transmission is sufficient to transmit all consolidated data to another neighbor. If the overall delay has to be kept as low as possible, scheduling sensors to avoid collisions while aggregating data becomes challenging.

The contribution of this paper is threefold. First, we give tight bounds for the complexity of data aggregation in static networks. In more details, we show that the problem remains NP-complete when the graph is of degree at most three. As it is trivial to solve the problem in static graphs of degree at most two, our result implies that the problem is intrinsically difficult for any practical setting. Second, we investigate the complexity of the same problem in a dynamic network, that is, a network whose topology can evolve through time. In the case of dynamic networks, we show that the problem is NP-complete even in the case where the graph is of degree at most two (and it is trivial to solve the problem when the graph is of degree at most one). Third, we give the first lower and upper bounds for the minimum data aggregation time in a dynamic graph.

We observe that even in a well-connected evolving graphs, the optimal solution cannot be found by a distributed algorithm or by a centralized algorithm that does not know the future. Thus we finally give the first approximation algorithm (centralized that knows the future) whose approximation factor is \(T(n-1)\) if there exists a bound *T* such that there is a journey (a path in a dynamic graph) for all pairs of nodes in every time interval \([t, t+T]\).

## Keywords

Data aggregation Dynamic graphs Complexity## Preview

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## References

- 1.Abshoff, S., Meyer auf der Heide, F.: Continuous aggregation in dynamic ad-hoc networks. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 194–209. Springer, Heidelberg (2014) Google Scholar
- 2.Annamalai, V., Gupta, S.K.S., Schwiebert, L.: On tree-based convergecasting in wireless sensor networks. In: 2003 IEEE Wireless Communications and Networking, 2003. WCNC 2003 , vol. 3, pp. 1942–1947. IEEE (2003)Google Scholar
- 3.Casteigts, A., Chaumette, S., Ferreira, A.: Characterizing topological assumptions of distributed algorithms in dynamic networks. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 126–140. Springer, Heidelberg (2010) CrossRefGoogle Scholar
- 4.Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Building fastest broadcast trees in periodically-varying graphs (2012). arXiv preprint arXiv:1204.3058
- 5.Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Shortest, fastest, and foremost broadcast in dynamic networks (2012). arXiv preprint arXiv:1210.3277
- 6.Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. In: Frey, H., Li, X., Ruehrup, S. (eds.) ADHOC-NOW 2011. LNCS, vol. 6811, pp. 346–359. Springer, Heidelberg (2011) CrossRefGoogle Scholar
- 7.Chen, X., Hu, X., Zhu, J.: Minimum data aggregation time problem in wireless sensor networks. In: Jia, X., Wu, J., He, Y. (eds.) MSN 2005. LNCS, vol. 3794, pp. 133–142. Springer, Heidelberg (2005) CrossRefGoogle Scholar
- 8.Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Mathematics
**86**(13), 165–177 (1990)MathSciNetCrossRefzbMATHGoogle Scholar - 9.Cornejo, A., Gilbert, S., Newport, C.: Aggregation in dynamic networks. In: Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing, pp. 195–204. ACM (2012)Google Scholar
- 10.Fasolo, E., Rossi, M., Widmer, J., Zorzi, M.: In-network aggregation techniques for wireless sensor networks: a survey. IEEE, Wireless Communications
**14**(2), 70–87 (2007)CrossRefGoogle Scholar - 11.Kuhn, F., Oshman, R.: Dynamic networks: Models and algorithms. SIGACT News
**42**(1), 82–96 (2011)CrossRefGoogle Scholar - 12.Lichtenstein, D.: Planar formulae and their uses. SIAM Journal on Computing
**11**(2), 329–343 (1982)MathSciNetCrossRefzbMATHGoogle Scholar - 13.Nguyen, T.D., Zalyubovskiy, V., Choo, H.: Efficient time latency of data aggregation based on neighboring dominators in wsns. In: 2011 IEEE Global Telecommunications Conference (GLOBECOM 2011), pp. 1–6. IEEE (2011)Google Scholar
- 14.Ren, M., Guo, L., Li, J.: A new scheduling algorithm for reducing data aggregation latency in wireless sensor networks. International Journal of Communications, Network & System Sciences
**3**(8) (2010)Google Scholar - 15.XiaoHua, X., Li, M., Mao, X.F., Tang, S., Wang, S.G.: A delay-efficient algorithm for data aggregation in multihop wireless sensor networks. IEEE Transactions on Parallel and Distributed Systems
**22**(1), 163–175 (2011)CrossRefGoogle Scholar - 16.Yu, B., Li, J., Li, Y.: Distributed data aggregation scheduling in wireless sensor networks. In: IEEE INFOCOM 2009, pp. 2159–2167. IEEE (2009)Google Scholar