Algorithm: Core sdwSSA

Input:$K,\gamma$ and c

1: mK ← 0

2: fork = 1 to Kdo

3:  t ← 0, $\mathbf{x}\leftarrow {\mathbf{x}}_0$, w ← 1

4:  evaluate all $a_j\left(\mathbf{x}\right)$ and calculate $a_0\left(\mathbf{x}\right)$

5:  evaluate all ${\gamma }_j\left({\pi }_j\left(\mathbf{x}\right)\right)$ and $b_j\left(\mathbf{x}\right)$; calculate $b_0\left(\mathbf{x}\right)$

6:  whilet ⩽ tfdo

7:  if$\mathbf{x}\in \mathcal{E}$then

8:   mK ← mK + w

9:   break out of the while loop

10:  endif

11:   generate two unit-interval uniform random numbers r1 and r2

12:   $\tau \leftarrow {b_0}^{-1}\left(\mathbf{x}\right)\ln (1/r_1)$

13:   j ← smallest integer satisfying ${\sum }_{i=1}^j{b}_i\left(\mathbf{x}\right)\ge r_2{b}_0\left(\mathbf{x}\right)$

14:   $w\leftarrow w\times {\left({\gamma }_j\left({\pi }_j\left(\mathbf{x}\right)\right)\right)}^{-1}\times \exp \left\{(b_0\left(\mathbf{x}\right)-a_0\left(\mathbf{x}\right))\tau \right\}$

15:   t ← t + τ, $\mathbf{x}\leftarrow \mathbf{x}+{\nu }_j$

16:   update all $a_j\left(\mathbf{x}\right)$ and $a_0\left(\mathbf{x}\right)$; recalculate ${\gamma }_j\left({\pi }_j\left(\mathbf{x}\right)\right)$, $b_j\left(\mathbf{x}\right)$ and $b_0\left(\mathbf{x}\right)$

17:  endwhile

18: endfor

19: return${\widehat{p}}_{sdwSSA}({\mathbf{x}}_0,\mathcal{E};t)=m_K/K$