From 0dc1a8ea20820168149cedaa14e223d4d31dc4b6 Mon Sep 17 00:00:00 2001 From: "Douglas B. Rumbaugh" Date: Sun, 6 Jul 2025 18:21:32 -0400 Subject: updates --- chapters/dynamization.tex | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) (limited to 'chapters/dynamization.tex') diff --git a/chapters/dynamization.tex b/chapters/dynamization.tex index 1012597..5e4cdec 100644 --- a/chapters/dynamization.tex +++ b/chapters/dynamization.tex @@ -33,7 +33,7 @@ the word \emph{query} \footnote{ The term query is often abused and used to refer to several related, but slightly different things. In the vernacular, a query can refer to either a) a general type of search - problem (as in "range query"), b) a specific instance of a search + problem (as in ``range query''), b) a specific instance of a search problem, or c) a program written in a query language. } is often used within the database systems literature: to refer to a @@ -302,6 +302,19 @@ blocks, we represent it with the notation $\mathscr{I} = \{\mathscr{I}_1, \ldots, \mathscr{I}_m\}$, where $\mathscr{I}_i$ is the $i$th block. \end{example} +In this example, the decomposition resulted in a reduction of the +worst-case insert cost. However, many decomposition schemes that we will +examine do not affect the worst-case cost, despite having notably better +performance in practice. As a result, it is more common to consider the +\emph{amortized} insertion cost, $I_A(n)$ when examining +dynamization. This cost function has the form, +\begin{equation*} + I_A(n) = \frac{B(n)}{n} \cdot \text{A} +\end{equation*} +where $\text{A}$ is the number of times that a record within the +structure participates in a reconstruction, often called the write +amplification. + Much of the existing work on dynamization has considered different decomposition methods for static data structures, and the effects that these methods have on insertion and query performance. However, before -- cgit v1.2.3