(1) **procedure ****RP**-**MR ** |

(2) Orient tree-shaped topology into a directed case with the root ; |

(3) Compute for each node using a bottom-up fashion; |

(4) Compute in a bottom-up fashion, where ; |

(5) Compute for each node by using **Lemma ( ****6)** in a top-down fashion; |

(6) Calculate the for the trajectories (shorter than ) that originate from node s by using **Lemma ( ****6)**, respectively; |

(7) Combine each pair of trajectories found in Step (6). Calculating the in the same way; |

(8) Computing the in-network data transmission cost for the path with maximum from the compound paths set; |

(9) return and ; |

(10) **end procedure** |