The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly involved, require synchronization and a lot of book keeping; this makes these algorithms impractical for resource-constrained networks such as ad hoc wireless sensor networks. In such networks, a

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... r has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energy-efficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate the theoretical results and show that the bounds are much better in practice. In particular, the quality of the tree found by the NNT algorithms is within a factor of 2 of the MST, but there is more than a ten-fold saving on the energy and about a five-fold saving on the number of messages sent compared to the classical messageoptimal algorithm of Gallager, Humblet, and Spira (GHS) [1]. Also, our algorithms are significantly simpler to implement compared to, for instance, the GHS algorithm. Thus, our results, the best of our knowledge, demonstrate the first such tradeoff between the quality of approximation and the energy required for building spanning trees on ad hoc networks, and motivates similar considerations for other important problems.