An exact algorithm for maximum lifetime data gathering tree without aggregation in wireless sensor networks
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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.
KeywordsWireless sensor networks Data gathering tree Maximum lifetime Exact algorithm Inapproximability
This work was partly supported by the New-Faculty Research Grant of Nanjing University of Aeronautics and Astronautics, China NSF Grants (61321491, 61373130, 61133006), NSF of Jiangsu Province Grant (BK20141319), and China 973 projects (2014CB340303, 2012CB316201).
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