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This work was supported by National Natural Science Foundation of China (Grant No. 61376032) and Tianjin Science and Technology Project of China (Grant No. 15ZCZDGX00180).
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Figure 1
(a) Procedure of DPOA; (b) procedure of DCDPOA; (c) simulation results; (d) ET of three algorithms.
$~S_{B}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~8,~1~\le~j~\le~8,~~i,j~\in~2~\mathbb{N}~\right\}~$; |
$~P_{B}~\Leftarrow~{\rm~CM}(S_{B}~)~$; |
$~w~\Leftarrow~8~$, $~h~\Leftarrow~8~$; |
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$~S_{\rm~ER}~\Leftarrow~\left\{~\left.~S(i,h+1)~\right|~1~\le~i~\le~8,~~i~\in~2\mathbb{N}+1~\right\}~$; |
$~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~ER}~)~$; |
$~h~\Leftarrow~h+2~$; |
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$~S_{\rm~EC}~\Leftarrow~\left\{~\left.~S(w+1,j)~\right|~1~\le~j~\le~H,~~j~\in~2\mathbb{N}+1~\right\}~$; |
$~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~EC}~)~$; |
$~w~\Leftarrow~w+2~$; |
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$~S_{\rm~EC}~\Leftarrow~\left\{~\left.~S(w+1,j)~\right|~1~\le~j~\le~8,~~j~\in~2\mathbb{N}+1~\right\}~$; |
$~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~EC}~)~$; |
$~w~\Leftarrow~w+2~$; |
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$~S_{\rm~ER}~\Leftarrow~\left\{~\left.~S(i,h+1)~\right|~1~\le~i~\le~W,~~i~\in~2\mathbb{N}+1~\right\}~$; |
$~P_{B}~\Leftarrow~{\rm~CM}(P_{B},~S_{\rm~ER}~)~$; |
$~h~\Leftarrow~h+2~$; |
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$~P_{F}~\Leftarrow~P_{B}~$. |
Solve $~\begin{cases} w~\times~N~+~4~\times~(N-1)~+p=W,~\\ N~\in~\mathbb{N},~~w,p~\in~2\mathbb{N}, \end{cases}~$and$~\begin{cases} h~\times~M~+~4~\times~(M-1)~+q=H,~\\ M~\in~\mathbb{N},~~h,q~\in~2\mathbb{N}, \end{cases}~$ get suitable $~N,w,p,M,h,q~$; |
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$~P_{a}~\Leftarrow~{\rm~DP}(w,h)~$; |
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$~P_{b}~\Leftarrow~P_{a}~$; |
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$~S_{\rm~CH}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~w,~h~\le~j~\le~h+4,\right.~$ $~~~~~~~~~~~\left.~i,~j~\in~2~\mathbb{N}+1~\right\}~$; |
$~P_{b}~\Leftarrow~{\rm~DP}(P_{a},~S_{\rm~CH},~P_{b})~$; |
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$~P_{c}~\Leftarrow~P_{b}~$; |
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$~S_{\rm~CV}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~j~\le~\left[~h~\times~M~+~4~\times~(M-1)~\right],~\right.~$$~\left.~~~~~~~~~~~~~w~\le~i~\le~w+4,~~i,~j~\in~2~\mathbb{N}+1~\right\}~$; |
$~P_{c}~\Leftarrow~{\rm~DP}(P_{b},~S_{\rm~CV},~P_{c})~$; |
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$~S_{\rm~RV}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~1~\le~i~\le~\left[~w~\times~N~+~4~\times~(N-1)~\right],~\right.~$ $~~~~~~~~~~~~\left[~h~\times~M~+~4~\times~(M-1)~\right]~\le~j~\le~H,~$ $~\left.~~~~~~~~~~~~i,j~\in~2~\mathbb{N}+1~\right\}~$; |
$~P_{c}~\Leftarrow~{\rm~DP}(P_{c},~S_{\rm~RV})~$; |
$~S_{\rm~RH}~\Leftarrow~\left\{~\left.~S(i,j)~\right|~\left[~w~\times~N~+~4~\times~(N-1)~\right]~\le~i~\le~W,~\right.~$ $~\left.~~~~~~~~~~~~~1~\le~j~\le~H,~~i,j~\in~2~\mathbb{N}+1~\right\}~$; |
$~P_{c}~\Leftarrow~{\rm~DP}(P_{c},~S_{\rm~RH})~$; |
$~P_{F}~\Leftarrow~P_{c}~$. |
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