11 Building Maximum Lifetime Shortest Path Data Aggregation Trees in Wireless Sensor Networks MENGFAN SHAN, GUIHAI CHEN, DIJUN LUO, XIAOJUN ZHU, and XIAOBING WU, Nanjing University In wireless sensor networks, the spanning tree is usually used as a routing structure to collect data. In some situations, nodes do in-network aggregation to reduce transmissions, save energy, and maximize network lifetime. Because of the restricted energy of sensor nodes, how to build an aggregation tree of maximum lifetime is an important issue. It has been proved to be NP-complete in previous works. As shortest path spanning trees intuitively have short delay, it is imperative to find an energy-efficient shortest path tree for time-critical applications. In this article, we first study the problem of building maximum lifetime shortest path aggregation trees in wireless sensor networks. We show that when restricted to shortest path trees, building maximum lifetime aggregation trees can be solved in polynomial time. We present a centralized algorithm and design a distributed protocol for building such trees. Simulation results show that our ap- proaches greatly improve the lifetime of the network and are very effective compared to other solutions. We extend our discussion to networks without aggregation and present interesting results. Categories and Subject Descriptors: C.2.2 [Computer-Communication Networks]: Network Protocols General Terms: Design, Algorithms, Performance Additional Key Words and Phrases: Wireless sensor networks, media access control, maximum lifetime, load balance ACM Reference Format: Mengfan Shan, Guihai Chen, Dijun Luo, Xiaojun Zhu, and Xiaobing Wu. 2014. Building maximum lifetime shortest path data aggregation trees in wireless sensor networks. ACM Trans. Sensor Netw. 11, 1, Article 11 (June 2014), 24 pages. DOI: http://dx.doi.org/10.1145/2629662 1. INTRODUCTION Data collection is an important operation in many wireless sensor network (WSN) applications, such as structure maintenance [Xu et al. 2004], environment monitoring [Liu et al. 2013], and habitat monitoring [Mainwaring et al. 2002]. Some divisible functions [Giridhar and Kumar 2005] (e.g., SUM, MAX, MIN, AVERAGE) are widely A preliminary version of this article was presented in Proceedings of the IEEE International Conference on Computer Communications (INFOCOM’11) [Luo et al. 2011]. This work was partly supported by the National Natural Science Foundation of China under grants 61133006, 61321491, and 61373130 and the National Basic Research Program of China (973 Program) under grants 2014CB340300 and 2012CB316200. X. Zhu was partly supported by the program B for Outstanding Ph.D. Candidate of Nanjing University under grant 201301B014. Authors’ addresses: M. Shan, G. Chen (corresponding author), D. Luo, X. Zhu, and X. Wu, State Key Lab for Novel Software Technology, Department of Computer Science and Technology, Nanjing University, Nanjing 210023, China, X. Zhu is also with the College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; email: nju.mfshan@gmail.com, gchen@nju.edu.cn, {luodijun, gxjzhu}@gmail.com, and wuxb@nju.edu.cn. Permission to make digital or hard copies of part or all 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 show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. c  2014 ACM 1550-4859/2014/06-ART11 $15.00 DOI: http://dx.doi.org/10.1145/2629662 ACM Transactions on Sensor Networks, Vol. 11, No. 1, Article 11, Publication date: June 2014.