\section{Conclusion}
\label{sec:conclusion}

This chapter discussed the creation of a framework for the dynamic extension of
static indexes designed for various sampling problems. Specifically, extensions
were created for the alias structure (WSS), the in-memory ISAM tree (IRS), and
the alias-augmented B+tree (WIRS). In each case, the SSIs were extended
successfully with support for updates and deletes, without compromising their
sampling performance advantage relative to existing dynamic baselines. This was
accomplished by leveraging ideas borrowed from the Bentley-Saxe method and the
design space of the LSM tree to divide the static index into multiple shards,
which could be individually reconstructed in a systematic fashion to
accommodate new data. This framework provides a large design space for trading
between update performance, sampling performance, and memory usage, which was
explored experimentally. The resulting extended indexes were shown to approach
or match the insertion performance of the B+tree, while simultaneously
performing significantly faster in sampling operations under most situations.