Abstract
Wireless sensor networks usually adopt a tree structure for routing, where each node sends and forwards messages to its parent. However, lifetime maximization with tree routing structure is NP-hard, and all algorithms attempting to find the optimal solution run in exponential time unless \(P=\mathrm{NP}\). This paper revisits the problem of non-tree routing structure, where a node can send different messages to different neighbors. Though lifetime maximization with non-tree routing can be solved in polynomial time, the existing method transforms it into a series of maximum flow problems, which are either complicated or with high running time. This paper proposes an algorithm with O(mn) running time, where m is the number of edges and n is the number of nodes. The heart of the algorithm is a method to find a routing path from any node to the sink in O(m) time without disconnecting existing routing paths. The proposed algorithm is also suitable for distributed implementation. When a node fails, each influenced node can establish a new routing path in O(m) time. Simulations are conducted to compare the optimal lifetimes of tree structure and non-tree structure on random networks. The results verify the effectiveness of the proposed algorithm.
Similar content being viewed by others
References
Buragohain C, Agrawal D, Suri S (2005) Power aware routing for sensor databases. In: Proceedings of INFOCOM
Liang J, Wang J, Cao J, Chen J, Lu M (2010) An efficient algorithm for constructing maximum lifetime tree for data gathering without aggregation in wireless sensor networks. In: Proceedings of INFOCOM
Zhu X, Wu X, Chen G (2015) An exact algorithm for maximum lifetime data gathering tree without aggregation in wireless sensor networks. Wirel Netw 21(1):281–295
Cao P, Zhu X (2018) Speeding up exact algorithms for maximizing lifetime of WSNs using multiple cores. Wirel Commun Mob Comput 2018:1–12
Chen J, Kleinberg RD, Lovász L, Rajaraman R, Sundaram R, Vetta A (2007) (Almost) tight bounds and existence theorems for single-commodity confluent flows. J ACM 54(4):16
Ma X, Zhu X, Chen B (2017) Exact algorithms for maximizing lifetime of WSNs using integer linear programming. In: Proceedings of WCNC
Wu Y, Mao Z, Fahmy S, Shroff N (2010) Constructing maximum-lifetime data-gathering forests in sensor networks. IEEE/ACM Trans Netw 18(5):1571–1584
Zhu X, Chen G, Tang S, Wu X, Chen B (2016) Fast approximation algorithm for maximum lifetime aggregation trees in wireless sensor networks. INFORMS J Comput 28(3):417–431
Zhu X, Tang S. Exact algorithms for the minimum load spanning tree problem. INFORMS J Comput (in press)
Shan M, Chen G, Luo D, Zhu X, Wu X (2014) Building maximum lifetime shortest path data aggregation trees in wireless sensor networks. ACM Trans Sens Netw 11(1):1–24
Fürer M, Raghavachari B (1994) Approximating the minimum-degree Steiner tree to within one of optimal. J Algorithms 17(3):409–423
Singh M, Lau LC (2015) Approximating minimum bounded degree spanning trees to within one of optimal. J ACM 62(1):1
Pal A, Jolfaei A (2020) On the lifetime of asynchronous software defined wireless sensor networks. IEEE Internet Things J 7(7):6069–6077
Fariborzi H, Moghavvemi M (2009) Eamtr: energy aware multi-tree routing for wireless sensor networks. IET Commun 3(6):733–739
Zhu X, Tang S. A branch and bound algorithm for building optimal data gathering tree in wireless sensor networks. INFORMS J Comput (in press). https://github.com/Xiaojun-Zhu/BranchBoundforWSN
Acknowledgements
This work was supported by the National Natural Science Foundation of China (61972199,61502232).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhu, X. Revisiting non-tree routing for maximum lifetime data gathering in wireless sensor networks. J Supercomput 77, 8927–8945 (2021). https://doi.org/10.1007/s11227-021-03621-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-021-03621-x