Algorithm 2 SFDM1

Input:Stream $X=X_1\cup X_2$, distance metric $d(·,·)$, parameter $\epsilon \in (0,1)$, size constraints $k_1,k_2\in {\mathbb{Z}}^{+}$ ($k=k_1+k_2$) Output: A set $S\subseteq X$ s.t. $|S\cap X_i|=k_i$ for $i\in \{1,2\}$ ▹Stream processing 1:$\mathcal{U}=\{\frac{d_{min}}{{(1-\epsilon )}^j}:j\in {\mathbb{Z}}_0^{+}\wedge {(1-\epsilon )}^j\ge \frac{d_{min}}{d_{max}}\}$ 2:Initialize $S_{\mu },S_{\mu ,i}=\varnothing$ for every $\mu \in \mathcal{U}$ and $i\in \{1,2\}$ 3:for all $x\in X$ do 4:    Run Lines 3–6 of Algorithm 1 to update $S_{\mu }$ w.r.t. x 5:    if $c\left(x\right)=i$ then 6:        Run Lines 3–6 of Algorithm 1 to update $S_{\mu ,i}$ w.r.t. x with size constraint $k_i$ ▹Post-processing 7:${\mathcal{U}}^{\prime }=\{\mu \in \mathcal{U}:\left|S_{\mu }\right|=k\wedge \left|S_{\mu ,i}\right|=k_i,\forall i\in \{1,2\}\}$ 8:for all $\mu \in {\mathcal{U}}^{\prime }$ do 9:    if $|S_{\mu }\cap X_i|<k_i$ for some $i\in \{1,2\}$ then 10:        while $|S_{\mu }\cap X_i|<k_i$ do 11:           $x^{+}\leftarrow {arg\; max}_{x\in S_{\mu ,i}}d(x,S_{\mu }\cap X_i)$ 12:           $S_{\mu }\leftarrow S_{\mu }\cup \left\{x^{+}\right\}$ 13:        while $\left|S_{\mu }\right|>k$ do 14:           $x^{-}\leftarrow {arg\; min}_{x\in S_{\mu }\setminus X_i}d(x,S_{\mu }\cap X_i)$ 15:           $S_{\mu }\leftarrow S_{\mu }\setminus \left\{x^{-}\right\}$ 16:return $S\leftarrow {arg\; max}_{\mu \in {\mathcal{U}}^{\prime }}div\left(S_{\mu }\right)$