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In this paper, power minimization for Poisson distributed random relay networks in Rayleigh fading channels is considered. We investigate two power allocation methods; one is a minimum power allocation (MPA) strategy and the other is an equal outage power allocation (EOPA) strategy. We analyze the total transmit power of two allocation methods under the given end-to-end outage probability constraint. Our results show that the MPA achieves more power saving than EOPA, and the power saving is more significant as the number of relay nodes increases.