15

continue

16

if $\text{wSupCnt}\left(N,D_{\text{clean}}\right)\ge \frac{\left|D\right|}{{\left({\text{wSupCnt}}_{N,D_{\text{clean}}}^{\max }+k\right)}^2\ast {\lambda }^2}-k$ then

17

continue

18

$D_{\text{vert}}\left[N\right]\Leftarrow \varnothing$ //generating the next layer of the searching tree

19

for all $m\in \mathcal{I}$ in such that $m>n$ do

20

$C\Leftarrow \mathrm{cov}\left(\left\{n\right\},D\right)\cap \mathrm{cov}\left(\left\{m\right\},D\right)$

21

$M\Leftarrow N\cup \left\{m\right\}$

22

$\text{wSupCnt}\left(M,D\right)\Leftarrow {\omega }_C\left|C\right|$

23

$\text{wSupCnt}\left(M,D_{\text{clean}}\right)\Leftarrow \text{wSupCnt}\left(M,D\right)-\text{wSupCnt}\left(M,D_{\text{dirty}}\right)$

24

if $\sqrt{\text{wSupCnt}\left(N,D\right)}-\sqrt{\text{wSupCnt}\left(M,D\right)}\ge {\lambda }^{-\frac{1}{2}}-\sqrt{{\text{wSupCnt}}_M^{\max }}-\frac{k}{\left|D\right|}$ then

25

$D_{\text{vert}}\left[N\right]\Leftarrow D_{\text{vert}}\left[N\right]\cup \left\{\left(m,C\right)\right\}$

26

$\text{QAbNI}\Leftarrow \text{QAbNI}\cup \text{QAbNIMiner}\left(D_{\text{vert}}\left[N\right],N,\lambda ,k\right)$

27

return QAbNI