From 432a7fd7da164841a2ad755b839de1e65244944d Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Tue, 3 Jun 2025 12:00:40 -0400
Subject: updates

---
 chapters/design-space.tex | 26 +++++++++++++++++++-------
 1 file changed, 19 insertions(+), 7 deletions(-)

(limited to 'chapters/design-space.tex')

diff --git a/chapters/design-space.tex b/chapters/design-space.tex
index 32d9b9c..952be42 100644
--- a/chapters/design-space.tex
+++ b/chapters/design-space.tex
@@ -730,7 +730,7 @@ and VPTree.
 \begin{figure}
 \centering
 \subfloat[ISAM Tree Range Count]{\includegraphics[width=.5\textwidth]{img/design-space/isam-parm-sweep.pdf} \label{fig:design-isam-tradeoff}} 
-\subfloat[VPTree $k$-NN]{\includegraphics[width=.5\textwidth]{img/design-space/selectivity-sweep.pdf} \label{fig:design-knn-tradeoff}} \\
+\subfloat[VPTree $k$-NN]{\includegraphics[width=.5\textwidth]{img/design-space/knn-parm-sweep.pdf} \label{fig:design-knn-tradeoff}} \\
 \caption{Insertion Throughput vs. Query Latency}
 \label{fig:design-tradeoff}
 \end{figure}
@@ -757,12 +757,24 @@ in scale factor have very little effect. However, level's insertion
 performance degrades linearly with scale factor, and this is well
 demonstrated in the plot.
 
-The Bentley-Saxe method appears to follow a very similar trend to that
-of leveling, albeit with even more dramatic performance degradation as
-the scale factor is increased. Generally it seems to be a strictly worse
-alternative to leveling in all but its best-case query cost, and we will
-omit it from our tests moving forward as a result.
-
+The store is a bit clearer in Figure~\ref{fig:design-knn-tradeoff}. The
+VPTree has a much greater construction time, both asymptotically and
+in absolute terms, and the average query latency is also significantly
+greater. These result in the configuration changes showing much more
+significant changes in performance, and present us with a far clearer
+trade-off space. The same general trends hold as in ISAM, just amplified.
+Leveling has better query performance than tiering and sees increased
+query performance and decreased insert performance as the scale factor
+increases. Tiering has better insertion performance and worse query
+performance than leveling, and sees improved insert and worstening
+query performance as the scale factor is increased. The Bentley-Saxe
+method shows similar trends to leveling.
+
+In general, the Bentley-Saxe method appears to follow a very similar
+trend to that of leveling, albeit with even more dramatic performance
+degradation as the scale factor is increased. Generally it seems to be
+a strictly worse alternative to leveling in all but its best-case query
+cost, and we will omit it from our tests moving forward as a result.
 
 \subsection{Query Size Effects}
 
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