From 5ffc53e69e956054fdefd1fe193e00eee705dcab Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Mon, 12 May 2025 19:59:26 -0400
Subject: Updates

---
 chapters/sigmod23/conclusion.tex | 33 +++++++++++++++++++--------------
 1 file changed, 19 insertions(+), 14 deletions(-)

(limited to 'chapters/sigmod23/conclusion.tex')

diff --git a/chapters/sigmod23/conclusion.tex b/chapters/sigmod23/conclusion.tex
index de6bffc..f350cfd 100644
--- a/chapters/sigmod23/conclusion.tex
+++ b/chapters/sigmod23/conclusion.tex
@@ -1,17 +1,22 @@
 \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.
-- 
cgit v1.2.3

