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<p><b>Abstract</b>—In this paper, we propose a family of structures, namely, <tmath>k{\hbox{-}}{\rm{localized}}</tmath> minimum spanning tree (<tmath>{\rm{LMST}}_k</tmath>) for topology control and broadcasting in wireless ad hoc networks. We give an efficient localized method to construct <tmath>{\rm{LMST}}_k</tmath> using only <tmath>O(n)</tmath> messages under the local-broadcast communication model, i.e., the signal sent by each node will be received by all nodes within the node's transmission range. We also analytically prove that the node degree of the structure <tmath>{\rm{LMST}}_k</tmath> is at most <tmath>6</tmath>, <tmath>{\rm{LMST}}_k</tmath> is connected and planar and, more importantly, the total edge length of the <tmath>{\rm{LMST}}_k</tmath> is within a constant factor of that of the minimum spanning tree when <tmath>k \ge 2</tmath> (called <it>low weighted</it> hereafter). We then propose another low weighted structure, called <it>Incident MST and RNG Graph</it> (IMRG), that can be locally constructed using at most <tmath>13n</tmath> messages under the local broadcast communication model. Test results are corroborated in the simulation study. We study the performance of our structures in terms of the total power consumption for broadcasting, the maximum node power needed to maintain the network connectivity. We theoretically prove that our structures are asymptotically the best possible for broadcasting among all locally constructed structures. Our simulations show that our new structures outperform previous locally constructed structures in terms of broadcasting and power assignment for connectivity.</p>
Localized algorithms, broadcasting, topology control, minimum spanning tree, wireless ad hoc networks.

Y. Wang, X. Li and W. Song, "Applications of k-Local MST for Topology Control and Broadcasting in Wireless Ad Hoc Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 15, no. , pp. 1057-1069, 2004.
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