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Diffstat (limited to 'chapters/sigmod23/examples.tex')
| -rw-r--r-- | chapters/sigmod23/examples.tex | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/chapters/sigmod23/examples.tex b/chapters/sigmod23/examples.tex index 4e7f9ac..32807e1 100644 --- a/chapters/sigmod23/examples.tex +++ b/chapters/sigmod23/examples.tex @@ -74,7 +74,7 @@ makes progress towards removing it. \subsection{Independent Range Sampling (ISAM Tree)} \label{ssec:irs-struct} We will next considered independent range sampling. For this decomposable -sampling problem, we use the ISAM Tree for the SSI. Because our shards are +sampling problem, we use the ISAM tree for the SSI. Because our shards are static, we can build highly compact and efficient ISAM trees by storing the records directly in a sorted array. So long as the leaf node size is a multiple of the record size, this array can be treated as a sequence of @@ -106,7 +106,7 @@ operations are, \text{Worst-case Tagged Delete:} \quad &O\left(\log_s n \log_f n\right) \end{align*} where $R(n) \in \Theta(1)$ for tagging and $R(n) \in \Theta(\log_s n \log_f n)$ -for tombstones and $f$ is the fanout of the ISAM Tree. +for tombstones and $f$ is the fanout of the ISAM tree. \subsection{Weighted Independent Range Sampling (Alias-augmented B+Tree)} @@ -114,13 +114,13 @@ for tombstones and $f$ is the fanout of the ISAM Tree. \label{ssec:wirs-struct} As a final example of applying this framework, we consider WIRS. This is a decomposable sampling problem that can be answered using the -alias-augmented B+Tree structure~\cite{tao22, afshani17,hu14}. This +alias-augmented B+tree structure~\cite{tao22, afshani17,hu14}. This data structure is built over sorted data, but can be bulk-loaded from this data in linear time, resulting in costs of $B(n) \in \Theta(n \log n)$ and $B_M(n) \in \Theta(n)$, though the constant factors associated with these functions are quite high, as each bulk-loading requires multiple -linear-time operations for building both the B+Tree and the alias -structures, among other things. As it is built on a B+Tree, the structure +linear-time operations for building both the B+tree and the alias +structures, among other things. As it is built on a B+tree, the structure supports $L(n) \in \Theta(\log n)$ point lookups. Answering sampling queries requires $P(n) \in \Theta(\log n)$ pre-processing time to establish the query interval, during which the weight of the interval |