From 33bc7e620276f4269ee5f1820e5477135e020b3f Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Sun, 8 Jun 2025 15:04:00 -0400
Subject: Julia updates v2

---
 chapters/sigmod23/framework.tex | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

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

diff --git a/chapters/sigmod23/framework.tex b/chapters/sigmod23/framework.tex
index d51c2cb..b3a8215 100644
--- a/chapters/sigmod23/framework.tex
+++ b/chapters/sigmod23/framework.tex
@@ -532,7 +532,7 @@ rates, buffering, sub-partitioning of structures to allow finer-grained
 reconstruction~\cite{dayan22}, and approaches for allocating resources to
 auxiliary structures attached to the main ones for accelerating certain
 types of query~\cite{dayan18-1, zhu21, monkey}. This work is discussed
-in greater depth in Chapter~\ref{chap:related-work}
+in greater depth in Chapter~\ref{chap:related-work}.
 
 Many of the elements within the LSM Tree design space are based upon the
 specifics of the data structure itself, and are not applicable to our
@@ -561,7 +561,7 @@ the case of sampling this isn't a serious problem. The implications of
 this will be discussed in Section~\ref{ssec:sampling-cost-funcs}. The
 size of this buffer, $N_B$ is a user-specified constant. Block capacities
 are defined in terms of multiples of $N_B$, such that each buffer flush
-corresponds to an insert in the traditioanl Bentley-Saxe method. Thus,
+corresponds to an insert in the traditional Bentley-Saxe method. Thus,
 rather than the $i$th block containing $2^i$ records, it contains $N_B
 \cdot 2^i$ records. We call this unsorted array the \emph{mutable buffer}.
 
@@ -750,8 +750,8 @@ operations must be used, the the cost becomes $I_a(n) \in
 \Paragraph{Delete.} The framework supports both tombstone and tagged
 deletes, each with different performance. Using tombstones, the cost
 of a delete is identical to that of an insert. When using tagging, the
-cost of a delete is the same as cost of doing a point lookup, as the
-"delete" itself is simply setting a bit in the header of the record,
+cost of a delete is the same as the cost of a point lookup, because the
+"delete" itself only sets a bit in the header of the record,
 once it has been located. There will be $\Theta(\log_s n)$ total shards
 in the structure, each with a look-up cost of $L(n)$ using either the
 SSI's native point-lookup, or an auxiliary hash table, and the lookup
-- 
cgit v1.2.3

