From f987e29e9f0ac8b2e491c67f2ecb38f7352660bd Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Tue, 10 Jun 2025 16:29:55 -0400
Subject: Began work on presentation

---
 chapters/beyond-dsp.tex | 38 ++++++++++++++++++++++++++++++++++----
 1 file changed, 34 insertions(+), 4 deletions(-)

(limited to 'chapters/beyond-dsp.tex')

diff --git a/chapters/beyond-dsp.tex b/chapters/beyond-dsp.tex
index a2e7abf..26f733c 100644
--- a/chapters/beyond-dsp.tex
+++ b/chapters/beyond-dsp.tex
@@ -351,6 +351,33 @@ interface, with the same performance as their specialized implementations.
 
 \subsection{Iterative Deletion Decomposability}
 \label{ssec:dyn-idsp}
+
+
+\begin{algorithm}[t]
+	\caption{Answering an Iterative Deletion Decomposable Search Problem}
+	\label{alg:dyn-query}
+	\KwIn{$q$: query parameters, $\mathscr{I}_1 \ldots \mathscr{I}_m$: blocks}
+	\KwOut{$R$: query results}
+	
+    $\mathscr{M} \gets \{\}$ \;
+    \For{$i \gets 1 \ldots m$}{$\mathscr{M} \gets \mathscr{M}\ \cup \texttt{local\_preproc}(\mathscr{I}_i, q)$ \;}
+    $(q_1, \ldots q_m) \gets \texttt{distribute\_query}(\mathscr{M}, q)$ \;
+    $R \gets \{\}; \ \ \texttt{rpt} \gets \bot$ \;
+    \Do{\texttt{rpt}}{
+		$r \gets \{\}$ \;
+        % the subscript in this one is wonky. Maybe do an array of Qs?
+		\For{$i \gets 1\ldots m$}{$r \gets r \cup \texttt{local\_query}(\mathscr{I}_i, q_i)$ \;}
+        %\Comment{For \red{name}, use \texttt{tombstone\_lookup} to remove all deleted records. }
+		%\If{\textbf{not} \texttt{SKIP\_DELETE\_FILTER}}{$locR \gets \texttt{filter\_deletes}(locR, S)$}
+        $R \gets R \cup \texttt{combine}(r)$ \;
+        $(\texttt{rpt}, q_1, \ldots,
+        q_m) \gets \texttt{repeat}(q, R, q_1,\ldots, q_m)$ \;
+	}
+    \Return{$R$}
+	
+\end{algorithm}
+
+
 We next turn out attention to support for deletes. Efficient delete
 support in Bentley-Saxe dynamization is provably impossible~\cite{saxe79},
 but, as discussed in Section~\ref{ssec:dyn-deletes} it is possible
@@ -396,9 +423,8 @@ class of search problem: \emph{iterative deletion decomposable} (IDSP). The
 IDSP definition expands eDSP with a fifth operation,
 
 \begin{itemize}
-	\item $\mathbftt{repeat}(\mathcal{Q}, \mathcal{R}, \mathcal{Q}_1, \ldots,
-        \mathcal{Q}_m) \to (\mathbb{B}, \mathcal{Q}_1, \ldots,
-        \mathcal{Q}_m)$ \\
+	\item $\mathbftt{repeat}(q, R, q_1, \ldots, q_m) \to
+    (\mathbb{B}, q_1, \ldots, q_m)$ \\
 	Evaluate the combined query result in light of the query. If
 	a repetition is necessary to satisfy constraints in the query
 	(e.g., result set size), optionally update the local queries as
@@ -428,7 +454,11 @@ records. This can be done, for example, using the full-reconstruction
 techniques in the literature~\cite{saxe79, merge-dsp, overmars83}
 or through proactively performing reconstructions, such as with the
 mechanism discussed in Section~\ref{sssec:sampling-rejection-bound},
-depending on the particulars of how deletes are implemented.
+depending on the particulars of how deletes are implemented. The
+full IDSP query algorithm is shown in Figure~\ref{alg:dyn-idsp-query}
+
+
+
 
 As an example of how IDSP can facilitate delete support for search
 problems, let's consider $k$-NN. This problem can be $C(n)$-deletion
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