Algorithm 3 AoI-MATP algorithm

1:Initialize ${\mathbf{w}}_m$, a small positive constant $\Delta \epsilon$, and $\epsilon ={\epsilon }_0$.    2:Calculate collection time ${\tau }_m^k$ between any two SNs.    3:repeat    4:   Run Algorithm 1 to obtain K, SN-CP association $\mathbf{o}$, and locations of CPs $\mathbf{L}$ with $\epsilon$.    5:   Calculate the optimal collection time $t_c^k$ in each CP k by (8) and flight time ${\mathbf{t}}_{\mathbf{F}}$ between any two CPs according to their distances.    6:   Run Algorithm 2 to obtain the visiting sequence $\mathbf{q}$.    7:   Calculate the optimal peak AoI by (9) and (10).    8:   Update $\epsilon \leftarrow \epsilon -\Delta \epsilon$.    9:until $\epsilon <0$.  10:Find the minimum $Ao{I}_p^{*}$ with the optimal ${\epsilon }^{*}$, and the according optimal solutions $(K^{*},{\mathbf{L}}^{*},{\mathbf{q}}^{*},{\mathbf{o}}^{*})$ are all found.