Table 1: Notation used.
 ℵ The set of sensor nodes. Ł The set of links. 𝑅 The communication radius of sensor. ℜ The set of RPs. ℜ o p t The optimal set of RPs with minimum data transmission cost. 𝜆 The energy consumption parameter. 𝑠 The stationary point where the Sink is located. 𝐶 ( ℜ ) The total in-network communication cost. 𝐷 The maximum data collection delay. 𝑇 The network lifetime. 𝐸 The initial energy of each sensor. 𝐿 The maximum length of ME’s trajectory. 𝐺 The adjacent matrix of the tree-shaped topology. 𝑌 ( ℜ ) The length of trajectory composed of ℜ . 𝑒 The energy consumption for transmitting one data packet from a node to its neighbor. 𝑝 ( 𝑖 ) The multihop transmission link between the node 𝑖 and nearest RP. 𝑝 o p t The optimal data collection trajectory with minimum data transmission cost. 𝑟 ( 𝑖 ) Data generation rate (packet/min) at node 𝑖 . 𝑇 𝑣 The subtree which rooted at node 𝑣 . 𝜈 M E The average velocity of the Mobile Element. 𝑝 𝑖 , 𝑗 The path between node 𝑖 and node 𝑗 . 𝑙 ( 𝑖 , 𝑗 ) Wireless link between node 𝑖 and node 𝑗 . 𝑐 𝑙 ( 𝑖 , 𝑗 ) The ETX of link 𝑙 ( 𝑖 , 𝑗 ) ∈ Ł. 𝜄 o u t ( 𝑖 ) The sets of outgoing links at node 𝑖 . 𝜄 i n ( 𝑖 ) The sets of incoming links at node 𝑖 . 𝑐 𝑝 ( 𝑖 ) The ETX sum of the link between node i and corresponding RP, 𝑐 𝑝 ∑ ( 𝑖 ) = 𝑙 ∈ 𝑝 ( 𝑖 ) 𝑐 𝑙 . 𝜅 𝑣 The sum of the data rate at all the decedent nodes of 𝑣 , 𝜅 𝑣 = ∑ 𝑖 ∈ 𝑇 𝑣 𝑟 ( 𝑖 ) . 𝑐 s a v e ( 𝑝 𝑢 , 𝑣 ) We define 𝑐 s a v e ( 𝑝 𝑢 , 𝑣 ) = 𝐶 ( 𝑢 ) − 𝐶 ( ℜ ) , where ℜ = { 𝑢 , 𝑣 } . This equation can be paraphrased as how many transmission count can be saved after we extend the path from node 𝑢 to node 𝑣 .