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authorDouglas Rumbaugh <dbr4@psu.edu>2025-05-12 19:59:26 -0400
committerDouglas Rumbaugh <dbr4@psu.edu>2025-05-12 19:59:26 -0400
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\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.
+In this chapter, we discussed the creation of a dynamization system
+based upon the Bentley-Saxe method that can be used to create dynamized
+sampling data structures that outperform dynamic baselines and feature a
+configurable design space. Specifically, we discussed dynamized versions
+of the alias structure for weighted set sampling, the alias-augmented
+B+tree for weighted independent range sampling, and the ISAM tree for
+independent range sampling. In each case, the static structures were
+dynamized with support for inserts and deletes without compromising
+their query performance advantage over dynamic baselines, and while
+matching or exceeding the dynamic structures' insertion performance.
+
+The techniques proposed in chapter, however, are limited to a very
+specific class of data structures for addressing a very specific type
+of search problem. While these results are promising, they fall short
+of a general solution to data structure dynamization that addresses
+the limitations of classical dynamization techniques discussed in
+Chapter~\ref{chap:background}. In the next chapter, we will take several
+of the results of this chapter, generalize them, and apply them to a much
+wider range of data structures.