Since any mobile equipments is driven by a battery, minimization of consumption of battery power in modern multi-hop wireless communication system is one of the essential problems. This paper presented an algorithm for shortest electric-power-distance, where total battery power consumption from the sender to the final receiver is minimum. Some computer simulations on large-scale multi-hop wireless systems were performed. It is shown that the "the law of the least action (Fermat's principle)" is still hold in the case of the shortest electric-power-distance problem, which is the common principle of natural physics.
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