Algorithm 5 SWDM

Input:Stream X, distance metric $d(·,·)$, window size $w\in {\mathbb{Z}}^{+}$, parameter $\epsilon \in (0,1)$, solution size $k\in {\mathbb{Z}}^{+}$ Output: A set $S\subseteq W$ with $\left|S\right|=k$ 1:$\Lambda ,\mathcal{U}=\{\frac{d_{min}}{{(1-\epsilon )}^j}:j\in {\mathbb{Z}}_0^{+}\wedge {(1-\epsilon )}^j\ge \frac{d_{min}}{d_{max}}\}$ 2:for all$\lambda \in \Lambda$ and $\mu \in \mathcal{U}$ do 3:    Initialize $A_{\lambda ,\mu },A_{\lambda ,\mu }^{\prime }=\varnothing$ and $B_{\lambda ,\mu },B_{\lambda ,\mu }^{\prime }=\varnothing$ 4:for all $x\in X$ do 5:    for all $\lambda \in \Lambda$ do 6:        for all $\mu \in \mathcal{U}$ do 7:           if $\left|B_{\lambda ,\mu }\right|<k$ and $d(x,B_{\lambda ,\mu })\ge \mu$ then 8:               $B_{\lambda ,\mu }\leftarrow B_{\lambda ,\mu }\cup \left\{x\right\}$, $B_{\lambda ,\mu }^{\prime }\left[x\right]\leftarrow x$ 9:           else if $d(x,B_{\lambda ,\mu })<\mu$ then 10:               $y^{\prime }\leftarrow {arg\; min}_{y\in B_{\lambda ,\mu }}d(x,y)$, $B_{\lambda ,\mu }^{\prime }\left[y^{\prime }\right]\leftarrow x$ 11:           if $A_{\lambda ,\mu }\ne \varnothing$ and $d(x,A_{\lambda ,\mu })<\mu$ then 12:               $y^{\prime }\leftarrow {arg\; min}_{y\in A_{\lambda ,\mu }}d(x,y)$, $A_{\lambda ,\mu }^{\prime }\left[y^{\prime }\right]\leftarrow x$ 13:        if ${max}_{\mu \in \mathcal{U}:\left|B_{\lambda ,\mu }\right|=k}div\left(B_{\lambda ,\mu }\right)>\lambda$ then 14:           Remove x from each $B_{\lambda ,\mu },B_{\lambda ,\mu }^{\prime }$ 15:           $A_{\lambda ,\mu },A_{\lambda ,\mu }^{\prime }\leftarrow B_{\lambda ,\mu },B_{\lambda ,\mu }^{\prime }$ for each $\mu \in \mathcal{U}$ 16:           $B_{\lambda ,\mu },B_{\lambda ,\mu }^{\prime }\leftarrow \left\{x\right\}$ for each $\mu \in \mathcal{U}$ ▹Post-processing 17:$W\leftarrow \{x\in X:max\{1,\left|X\right|-w+1\}\le t(x)\le |X\left|\right\}$ 18:for all$\lambda \in \Lambda$ and $\mu \in \mathcal{U}$ do 19:    if $A_{\lambda ,\mu }\subseteq W$ then 20:        $S_{\lambda ,\mu }\leftarrow \mathsf{ALG}(k,A_{\lambda ,\mu }\cup B_{\lambda ,\mu })$ 21:    else if $B_{\lambda ,\mu }\subseteq W$ then 22:        $S_{\lambda ,\mu }\leftarrow \mathsf{ALG}(k,(W\cap A_{\lambda ,\mu }^{\prime })\cup B_{\lambda ,\mu })$ 23:return $S\leftarrow {arg\; max}_{\lambda \in \Lambda ,\mu \in \mathcal{U}:\left|S_{\lambda ,\mu }\right|=k}div\left(S_{\lambda ,\mu }\right)$