Book Chapter10.1007/3-540-45735-6_23
Fully Dynamic Spatial Approximation Trees
Gonzalo Navarro,Nora Susana Reyes +1 more
- 11 Sep 2002
- pp 254-270
TL;DR: A dynamic version of the sa-tree that handles insertions and deletions is presented, showing experimentally that the price of adding dynamism is rather low and the outcome is a much more practical data structure that can be useful in a wide range of applications.
read more
Abstract: The Spatial Approximation Tree (sa-tree) is a recently proposed data structure for searching in metric spaces. It has been shown that it compares favorably against alternative data structures in spaces of high dimension or queries with low selectivity. Its main drawbacks are: costly construction time, poor performance in low dimensional spaces or queries with high selectivity, and the fact of being a static data structure, that is, once built, one cannot add or delete elements. These facts rule it out for many interesting applications.In this paper we overcome these weaknesses. We present a dynamic version of the sa-tree that handles insertions and deletions, showing experimentally that the price of adding dynamism is rather low. This is remarkable by itself since very few data structures for metric spaces are fully dynamic. In addition, we show how to obtain large improvements in construction and search time for low dimensional spaces or highly selective queries. The outcome is a much more practical data structure that can be useful in a wide range of applications.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The Basic Principles of Metric Indexing
Magnus Lie Hetland
- 01 Jan 2009
TL;DR: This chapter describes several methods of similarity search, based on metric indexing, in terms of their common, underlying principles, and several approaches to creating lower bounds using the metric axioms are discussed.
Dynamic spatial approximation trees
TL;DR: Different methods to handle insertions and deletions on the sa--tree at low cost are studied, and the dynamic version significantly improves the search performance of sa--trees in virtually all cases.
Hilbert Exclusion: Improved Metric Search through Finite Isometric Embeddings
TL;DR: It is shown that many common metric spaces, notably including those using Euclidean and Jensen-Shannon distances, also have a stronger property, sometimes called the four-point property, and one in particular, which is named the Hilbert Exclusion property, allows any indexing mechanism which uses hyperplane partitioning to perform better.
Indexing Metric Spaces for Exact Similarity Search
07 Dec 2022
TL;DR: A comprehensive survey of existing metric indexes that support exact similarity search can be found in this article , where the authors summarize existing partitioning, pruning, and validation techniques used by metric indexes to support approximate similarity search, and provide the time and space complexity analyses of index construction.
An index data structure for searching in metric space databases
Roberto Uribe,Gonzalo Navarro,Ricardo J. Barrientos,Mauricio Marin +3 more
- 28 May 2006
TL;DR: Empirical results show that the EGNAT is suitable for conducting similarity searches on very large metric space databases, and it is shown that this data structure allows efficient parallelization on distributed memory parallel architectures.
References
Searching in metric spaces
TL;DR: A unified view of all the known proposals to organize metric spaces, so as to be able to understand them under a common framework, and presents a quantitative definition of the elusive concept of "intrinsic dimensionality".
1.4K
Searching in metric spaces by spatial approximation
Gonzalo Navarro
- 21 Sep 1999
TL;DR: This work proposes a new data structure, called sa-tree (“spatial approximation tree”), which is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures.
321
Searching in metric spaces by spatial approximation
Gonzalo Navarro
- 01 Aug 2002
TL;DR: In this article, the authors propose a data structure called sa-tree (SPatial approximation tree), which is based on approaching the searched objects spatially, that is, getting closer and closer to them.
273
Dynamic spatial approximation trees
Gonzalo Navarro,Nora Susana Reyes +1 more
- 01 Nov 2001
TL;DR: It is shown that it is viable to modify the sa-tree so as to permit fast insertions while keeping its good search efficiency, and specifically developed considering the particular properties of this data structure.
42
Multidimensional access methods
Volker Gaede,Oliver Günther +1 more
TL;DR: The class of point access methods, which are used to search sets of points in two or more dimensions, are presented and a discussion of theoretical and experimental results concerning the relative performance of various approaches are discussed.