\section{Conclusions and Future Work} 
\label{sec:Conclusions}

In this article, we proposed the HeightBL, an algorithm for \bl\ \fonions. 
The proposed \hbl\ introduces the following distinctive properties.
It is top-down, and organizes the elements to be inserted into the index in advance to define the best insertion order of these elements.
It also builds the structure by using samples to choose the pivots of the nodes.
Furthermore, it defines a strategy to estimate the ideal height that a \fonion\ should have, so that the final structure has approximately this estimated height.

The \hbl\ was validated through performance testes using real-world data with different volumes and dimensionalities.
The results showed that the \hbl\ generated very compact indices.
Compared with the \ee\ of the \fonion, the size of the index reduced from 53.42\% to 71.25\%.
The results also demonstrated that the \hbl\ greatly improved the similarity query processing in comparison to the \ee.
It was from 10.00\% to 99.04\% faster to process range queries and was from to 8.57\% to 30.00\% faster to process \knn\ queries.
It also reduced the number of distance calculations from 18.75\% to 99.94\% to process range queries and from 13.38\% to 51.66\% to process \knn\ queries.   
We can conclude that the \hbl\ fulfills the requirements of the \bl\ technique: it produces more compact indices and guarantees expressive performance gain in range and \knn\ query processing.

We are currently developing a bottom-up algorithm for \bl\ \fonions.
We also plan to run experiments using new real-world datasets with different metrics and characteristics, as well as to investigate experiments with synthetic data.
Furthermore, we plan to propose an algorithm that performs deletions of elements from the \fonion.
Another future work is to apply the \fonion\ and its \hbl\ to execute condition-extended similarity queries over complex data, such as those queries described in~\cite{SoaresKaster13}.




