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<p><b>Abstract</b>—We investigate the problem of minimum energy broadcasting in ad hoc networks where nodes have capability to adjust their transmission range. The minimal transmission energy needed for correct reception by neighbor at distance <tmath>r</tmath> is proportional to <tmath>r^\alpha + c_{{\rm{e}}}</tmath>, <tmath>\alpha</tmath>, and <tmath>c_{{\rm{e}}}</tmath> being two environment-dependent constants. We demonstrate the existence of an optimal transmission radius, computed with a hexagonal tiling of the network area, that minimizes the total power consumption for a broadcasting task. This theoretically computed value is experimentally confirmed. The existing localized protocols are inferior to existing centralized protocols for dense networks. We present two localized broadcasting protocols, based on derived "target” radius, that remain competitive for all network densities. The first one, TR-LBOP, computes the minimal radius needed for connectivity and increases it up to the target one after having applied a neighbor elimination scheme on a reduced subset of direct neighbors. In the second one, TRDS, each node first considers only neighbors whose distance is no greater than the target radius (which depends on the power consumption model used), and neighbors in a localized connected topological structure such as RNG or LMST. Then, a connected dominating set is constructed using this subgraph. Nodes not selected for the set may be sent to sleep mode. Nodes in selected dominating set apply TR-LBOP. This protocol is the first one to consider both activity scheduling and minimum energy consumption as one combined problem. Finally, some experimental results for both protocols are given, as well as comparisons with other existing protocols. Our analysis and protocols remain valid if energy needed for packet receptions is charged.</p>
Ad hoc networks, sensor networks, energy efficient broadcasting, optimal transmission radius, localized communication protocols.

D. Simplot-Ryl, F. Ingelrest and I. Stojmenovic, "Optimal Transmission Radius for Energy Efficient Broadcasting Protocols in Ad Hoc and Sensor Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 17, no. , pp. 536-547, 2006.
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