Minimum-Energy Mobile Wireless Networks Revisited
  We propose a protocol that, given a communication network, computes a subnetwork such that, for every pair $(u,v)$ of nodes connected in the original network, there is a minimum-energy path between $u$ and $v$ in the subnetwork (where a minimum-energy path is one that allows messages to be transmitted with a minimum use of energy). The network computed by our protocol is in general a subnetwork of the one computed by the protocol given in [13]. Moreover, our protocol is computationally simpler. We demonstrate the performance improvements obtained by using the subnetwork computed by our protocol through simulation. 
Erran L. Li and Joseph Y. Halpern