Table 1: Notation used.

The set of sensor nodes.
Ł The set of links.
𝑅 The communication radius of sensor.
The set of RPs.
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 ( ) 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 ( ) The length of trajectory composed of .
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 ( ) , where = { 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 .