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+\section{Related Work}

+\label{sec:related}

+

+The general IQS problem was first proposed by Hu, Qiao, and Tao~\cite{hu14} and

+has since been the subject of extensive research

+\cite{irsra,afshani17,xie21,aumuller20}. These papers involve the use of

+specialized indexes to assist in drawing samples efficiently from the result

+sets of specific types of query, and are largely focused on in-memory settings.

+A recent survey by Tao~\cite{tao22} acknowledged that dynamization remains a major

+challenge for efficient sampling indexes. There do exist specific examples of

+sampling indexes~\cite{hu14} designed to support dynamic updates, but they are

+specialized, and impractical due to their

+implementation complexity and high constant-factors in their cost functions. A

+static index for spatial independent range sampling~\cite{xie21} has been

+proposed with a dynamic extension similar to the one proposed in this paper, but the method was not

+generalized, and its design space was not explored. There are also

+weight-updatable implementations of the alias structure \cite{hagerup93,

+matias03, allendorf23} that function under various assumptions about the weight

+distribution. These are of limited utility in a database context as they do not

+support direct insertion or deletion of entries. Efforts have also been made to

+improve tree-traversal based sampling approaches. Notably, the AB-tree

+\cite{zhao22} extends tree-sampling with support for concurrent updates, which

+has been a historical pain point. 

+

+The Bentley-Saxe method was first proposed by Saxe and Bentley~\cite{saxe79}.

+Overmars and van Leeuwen extended this framework to provide better worst-case

+bounds~\cite{overmars81}, but their approach hurts common case performance by

+splitting reconstructions into small pieces and executing these pieces each

+time a record is inserted. Though not commonly used in database systems, the

+method has been applied to address specialized, problems, such as the creation

+of dynamic metric indexing structures~\cite{naidan14}, analysis of

+trajectories~\cite{custers19}, and genetic sequence search

+indexes~\cite{almodaresi23}.