3.2 Efficient Localized Node-Selection Algorithms

3.2.1 Reformulate the Node-Selection Optimization Problem

We know that when the number of neighbors involved in GOR is given, the denominator of the function images/c03_I0020.gif defined in Equation (3.2) is fixed, then maximizing images/c03_I0021.gif is equivalent to maximize its numerator. So we can find the suboptimal solution for each r = 1, 2,middot, N, then get a global optimal solution by picking the largest one of the suboptimal solutions. From this analysis, as the packet length Lpkt is fixed, combining Equation (3.1), the optimization problem in (3.3) is equivalent to

3.4 3.4

We now introduce the following corollary that can help us solve this optimization problem more efficiently.

 

Corollary 3.1 (Local maximum of M(r) is global maximum) Given the available next-hop node set images/c03_I0023.gif with images/c03_I0024.gif, the receiving energy consumption Erx > 0 and transmission energy consumption Etx > 0, the local ...

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