Wireless Networks

, Volume 21, Issue 1, pp 281–295

An exact algorithm for maximum lifetime data gathering tree without aggregation in wireless sensor networks


DOI: 10.1007/s11276-014-0784-0

Cite this article as:
Zhu, X., Wu, X. & Chen, G. Wireless Netw (2015) 21: 281. doi:10.1007/s11276-014-0784-0


In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NP-complete. In this paper, we prove that, unless P = NP, no polynomial-time algorithm can approximate the problem with a factor strictly greater than 2/3. The result even holds in the special case where all sensors have the same initial energy. Existing works for the problem focus on approximation algorithms, but these algorithms only find sub-optimal spanning trees and none of them can guarantee to find an optimal tree. We propose the first non-trivial exact algorithm to find an optimal spanning tree. Due to the NP-hardness nature of the problem, this proposed algorithm runs in exponential time in the worst case, but the consumed time is much less than enumerating all spanning trees. This is done by several techniques for speeding up the search. Featured techniques include how to grow the initial spanning tree and how to divide the problem into subproblems. The algorithm can handle small networks and be used as a benchmark for evaluating approximation algorithms.


Wireless sensor networks Data gathering tree Maximum lifetime Exact algorithm Inapproximability 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.College of Computer Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.State Key Laboratory for Novel Software TechnologyNanjing UniversityNanjingChina
  3. 3.Shanghai Key Laboratory of Scalable Computing and SystemsShanghai Jiao Tong UniversityShanghaiChina

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