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@@ -1,7 +1,7 @@
\subsection{Comparison to Baselines}
Next, we compared the performance of our dynamized sampling indices with
-Olken's method on an aggregate B+Tree. We also examine the query performance
+Olken's method on an aggregate B+tree. We also examine the query performance
of a single instance of the SSI in question to establish how much query
performance is lost in the dynamization. Unless otherwise specified,
IRS and WIRS queries are run with a selectivity of $0.1\%$. Additionally,
@@ -51,15 +51,15 @@ resulting in better performance.
In Figures~\ref{fig:wirs-insert} and \ref{fig:wirs-sample} we examine
the performed of \texttt{DE-WIRS} compared to \text{AGG B+tree} and an
-alias-augmented B+Tree. We see the same basic set of patterns in this
+alias-augmented B+tree. We see the same basic set of patterns in this
case as we did with WSS. \texttt{AGG B+Tree} defeats our dynamized
index on the \texttt{twitter} dataset, but loses on the others, in
terms of insertion performance. We can see that the alias-augmented
-B+Tree is much more expensive to build than an alias structure, and
+B+tree is much more expensive to build than an alias structure, and
so its insertion performance advantage is eroded somewhat compared to
the dynamic structure. For queries we see that the \texttt{AGG B+Tree}
performs similarly for WIRS sampling as it did for WSS sampling, but the
-alias-augmented B+Tree structure is quite a bit slower at WIRS than the
+alias-augmented B+tree structure is quite a bit slower at WIRS than the
alias structure was at WSS. This results in \texttt{DE-WIRS} defeating
the dynamic baseline by less of a margin in this test, but it still is
superior in terms of sampling performance, and is still quite close in
@@ -81,7 +81,7 @@ being introduced by the dynamization.
We next considered IRS queries. Figures~\ref{fig:irs-insert1} and
\ref{fig:irs-sample1} show the results of our testing of single-threaded
-\texttt{DE-IRS} running in-memory against the in-memory ISAM Tree and
+\texttt{DE-IRS} running in-memory against the in-memory ISAM tree and
\texttt{AGG B+tree}. The ISAM tree structure can be efficiently bulk-loaded,
which results in a much faster construction time than the alias structure
or alias-augmented B+tree. This gives it a significant update performance
@@ -112,7 +112,7 @@ to answer queries. However, as the sample set size increases, this cost
increasingly begins to pay off, with \texttt{DE-IRS} quickly defeating
the dynamic structure in average per-sample latency. One other interesting
note is the performance of the static ISAM tree, which begins on-par with
-the B+Tree, but also sees an improvement as the sample set size increases.
+the B+tree, but also sees an improvement as the sample set size increases.
This is because of cache effects. During the initial tree traversal, both
the B+tree and ISAM tree have a similar number of cache misses. However,
the ISAM tree needs to perform its traversal only once, and then samples