Algorithm 2. Client Selection. The server selects clients and adjusts client’s training data

• Input $$\begin{gathered} \mathcal{K}, \mathcal{N}=\left\{{\mathit{n}}_1, {\mathit{n}}_{2,}\dots , {\mathit{n}}_K\right\}{ \mathrm{client}}^{’}\mathrm{s} \mathrm{class} \mathrm{information} \mathrm{set}, {\theta }_{KLD} \mathrm{KLD} \mathrm{threshold}, \\ h \mathrm{maximum} \mathrm{number} \mathrm{of} \mathrm{selected} \mathrm{client},L \mathrm{number} \mathrm{of} \mathrm{classes} \end{gathered}$$ • Output $\mathrm{selected} \mathrm{client} \mathrm{class} \mathrm{information} \mathrm{set}$ ${\mathcal{S}}_{\mathrm{info}}$ = ${\left\{{\mathit{s}}_{1,r}, {\mathit{s}}_{2,r,}\dots , {\mathit{s}}_{h,r}\right\}}^T$ 1: initialize ${\mathcal{S}}_{\mathrm{info}}\leftarrow \varnothing ,\mathrm{data} \mathrm{volume} \mathrm{vector} {\mathit{v}}_r={\left[v_r^1,v_r^2, \dots , v_r^L\right]}^T$ 2: Sort $\mathcal{N}$ in descending order by the amount of data ${\displaystyle \sum }_{𝓁}^L{n}_k^{𝓁}, k\in \mathcal{N}$ 3: repeat 4:   for each $n_c\in \mathcal{N}$ do 5:    if ${\mathcal{S}}_{\mathrm{info}} \mathrm{is} \mathrm{empty}$ then 6:     for each $𝓁$, $𝓁$ = 1, 2, …, $L$ do 7:      $v_r^{𝓁} \leftarrow v_r^{𝓁}+n_c^{𝓁}$ 8:      $s_{c,r}^{𝓁}$ $\leftarrow n_c^{𝓁}$ 9:       end for 10:     $m$ $\leftarrow$ max(${\mathit{v}}_r$) //Maximum value among ${\mathit{v}}_r$ 11:     add ${\mathit{s}}_{c,r}$ in ${\mathcal{S}}_{\mathrm{info}}$ 12:    else 13:     $f\leftarrow$ ${\mathrm{argmin}}_{𝓁} \left(v_r\right)$ 14:     if $n_c^f>0$ then 15:      for each $𝓁$, $𝓁$ = 1, 2, …, $L$ do 16:       $v_r^{𝓁}\leftarrow$ $v_r^{𝓁}$ + min($m$—$v_r^{𝓁}$, $n_c^{𝓁}$) 17:       ${\mathit{s}}_{c,r}^{𝓁}$ $\leftarrow$ min($m$—$v_r^{𝓁}$, $n_c^{𝓁}$) 18:      end for 19:      add $s_{c,r}$ in ${\mathcal{S}}_{\mathrm{info}}$ 20:     end if 21:    end if 22:   end for 23: until $\left|{\mathcal{S}}_{\mathrm{info}}\right|==h \mathrm{or} D_{KL} \left(P_{v_r}│P_{\mathrm{uniform}}\right)<{\theta }_{KLD}$ 24: return ${\mathcal{S}}_{\mathrm{info}}$