Algorithm 3 Compress P into $P_{global}$

Input:P, $P_{local}$, $r_{pos}\in D_{i,j}$ Output:$P_{global}$ 1: Define $P^{\prime }={(p_{i,j}^{\prime })}_{m\times n}$: $$p_{i,j=}^{\prime }\left\{\begin{array}{cc}0& p_{i,j}=\infty \\ p_{i,j}& p_{i,j}\ne \infty \end{array}\right.$$ 2: Compress matrix $P^{\prime }$ into $3\times 3$ matrix $P_{global}^{\prime }=$ $$\left[\begin{array}{ccc}\frac{{\sum }_{a=1,b=1}^{a=i,b=j}{p}_{a,b}^{\prime }}{i\times j}& \frac{{\sum }_{a=1,b=1}^{a=i,b=n}{p}_{a,b}^{\prime }}{i\times n}& \frac{{\sum }_{a=1,b=j}^{a=i,b=n}{p}_{a,b}^{\prime }}{i\times (n-j+1)}\\ \frac{{\sum }_{a=1,b=1}^{a=m,b=j}{p}_{a,b}^{\prime }}{m\times j}& \infty & \frac{{\sum }_{a=1,b=j}^{a=m,b=n}{p}_{a,b}^{\prime }}{m\times (n-j+1)}\\ \frac{{\sum }_{a=i,b=1}^{a=m,b=j}{p}_{a,b}^{\prime }}{(m-i+1)\times j}& \frac{{\sum }_{a=i,b=1}^{a=m,b=n}{p}_{a,b}^{\prime }}{(m-i+1)\times n}& \frac{{\sum }_{a=i,b=j}^{a=m,b=n}{p}_{i,j}^{\prime }}{(m-i+1)\times (n-j+1)}\end{array}\right]$$ 3:Mapping $P_{local}$ to $P_{local}^{\prime }$ by replacing all elements not equal to ∞ into 0 4:$P_{global}=P_{local}^{\prime }+P_{global}^{\prime }$