Algorithm 3: A modified agglomerative hierarchical clustering.

Data: n points $P_1,\dots ,P_n$

Result: A parsimonious tree T for $P_1,\dots ,P_n$

$C_i\leftarrow P_i,i=1,\dots ,n$;

$E(T)\leftarrow \mathrm{\varnothing }$;

$labels\leftarrow \mathrm{\varnothing }$;

$C\leftarrow \{C_1,\dots ,C_n\}$;

while $|C|>1$ do

$D_{ij}\leftarrow d_{BC}(C_i,C_j)$ for $C_i,C_j\in C$;

${\hat{C}}_i,{\hat{C}}_j\leftarrow \arg \underset{C_i,C_j}{min}{D}_{ij}$;

${\hat{P}}_i,{\hat{P}}_j\leftarrow \arg \underset{x\in {\hat{C}}_i,y\in {\hat{C}}_j}{min}{d}_H(x,y)$;

$C\leftarrow C+{\hat{C}}_i\cup {\hat{C}}_j$;

$E(T)\leftarrow E(T)+\{({\hat{C}}_i,{\hat{C}}_i\cup {\hat{C}}_j),({\hat{C}}_j,{\hat{C}}_i\cup {\hat{C}}_j)\}$;

if ${\hat{C}}_i$ is a leaf then

$label({\hat{C}}_i)\leftarrow P_i$;

else

$label({\hat{C}}_i)\leftarrow {\hat{P}}_i$;

end

if ${\hat{C}}_j$ is a leaf then

$label({\hat{C}}_j)\leftarrow P_j$;

else

$label({\hat{C}}_j)\leftarrow {\hat{P}}_j$;

end

$labels\leftarrow labels+\{label({\hat{C}}_i),label({\hat{C}}_j)$;

$C\leftarrow C-\{{\hat{C}}_i,{\hat{C}}_j\}$;

end