From f3fb78badb07cc012a32c32102a3fa3b68269fed Mon Sep 17 00:00:00 2001
From: "Douglas B. Rumbaugh" <doug@douglasrumbaugh.com>
Date: Sun, 1 Jun 2025 15:19:20 -0400
Subject: conclusion

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 chapters/conclusion.tex | 55 ++++++++++++++++---------------------------------
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(limited to 'chapters/conclusion.tex')

diff --git a/chapters/conclusion.tex b/chapters/conclusion.tex
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 \chapter{Conclusion}
 \label{chap:conclusion}
 
-Using data structures, a wide range of analytical queries against large data
-sets can be accelerated. Unfortunately, these data structures must be
-concurrently updatable to ensure timely results, as the underlying data is
-frequently subject to change. This requirement for concurrent update support
-excludes many possible data structures from use in these contexts, and the
-creation of a data structure with update support is non-trivial.
+In this work, we have considered approaches for automatically
+adding support for concurrent updates to static data structures,
+for the purpose of reducing the amount of work necessary to produce a
+dynamic index. Classical dynamization techniques suffered from several
+limitations on supported data structures, as well as performance problems
+stemming from a lack of configurability and poor worst-case insertion
+performance. We have attempted to address these limitations.
 
-The framework proposed by this work would allow for existing data
-structures to be automatically extended with tunable support for
-concurrent updates, with potential for future work to add even more
-features. It is based on an extension of the Bentley-Saxe method,
-which supports updates in static structures by splitting the data
-structure into multiple partitions and systematically reconstructing
-them. The Bentley-Saxe method has been adjusted to utilize a different
-query interface, based on the newly proposed extended decomposability,
-which brings with it more efficient support for many types of search
-problems not well served by the original techniques. It also introduces
-two approaches for handling deletes, buffering of inserts, and a more
-tunable reconstruction strategy, as well as support for concurrency,
-none of which were present in the original method.
+The result of these efforts is a generalized dynamization framework built
+upon a set of novel mathematical results that allows for many static
+data structures to be automatically extended with tunable, concurrent
+insertion and deletion support, with bounded additional query cost. The
+technique expands on the base Bentley-Saxe method with new query interfaces
+to enable support for search problems that are not traditional decomposable,
+a tunable design space including buffering and alternative block layout
+polices to allow for trade-offs between insertion and query performance,
+and support for parallel reconstructions in a manner that effectively
+reduces the worst-case insertion cost while maintaining similar query
+performance. 
 
-Using this framework, many data structures and search problems can be
-used as the basis of an index, requiring only that they support the
-eDSP abstraction and can uniquely identify and locate each record. The
-creation of an index requires only a small amount of shim code between
-the structure and the framework (called a shard).
 
-The current version of the framework supports tunable, single-threaded
-updates, and has been experimentally validated to extend static data
-structures with update support, and maintain performance on-par
-with or better than existing dynamic alternatives for a number of
-complex search problems, including k-nearest neighbor and a variety
-of independent sampling problems. Beyond presenting these results,
-this work proposes the extension of this framework with support for
-concurrency with tail-latency mitigations, online and fine-grained
-tuning, and examining more sophisticated data partitioning schemes to
-ease certain challenges associated with large-scale reconstructions.
-The completion of this framework would be a major milestone in a larger
-project to vastly expand the capabilities of database management systems
-through the use of more complex data access primitives.
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