An algorithm for finding nearest neighbours in (approximately) constant average time
Pattern Recognition Letters
Multidimensional access methods
ACM Computing Surveys (CSUR)
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
ACM Computing Surveys (CSUR)
Modern Information Retrieval
Improved Greedy Algorithms for Constructing Sparse Geometric Spanners
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Probabilistic Proximity Searching Algorithms Based on Compact Partitions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
A Probabilistic Spell for the Curse of Dimensionality
ALENEX '01 Revised Papers from the Third International Workshop on Algorithm Engineering and Experimentation
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
t-Spanners for metric space searching
Data & Knowledge Engineering
Sparse geometric graphs with small dilation
Computational Geometry: Theory and Applications
Experimental study of geometric t-spanners
Journal of Experimental Algorithmics (JEA)
Simple space-time trade-offs for AESA
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Journal of Discrete Algorithms
Indexing methods for approximate dictionary searching: Comparative analysis
Journal of Experimental Algorithmics (JEA)
On the least cost for proximity searching in metric spaces
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
I/O-Efficiently pruning dense spanners
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Experimental study of geometric t-spanners
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Sparse geometric graphs with small dilation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Using the k-nearest neighbor graph for proximity searching in metric spaces
SPIRE'05 Proceedings of the 12th international conference on String Processing and Information Retrieval
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A t-spanner, a subgraph that approximates graph distances within a precision factor t, is a well known concept in graph theory. In this paper we use it in a novel way, namely as a data structure for searching metric spaces. The key idea is to consider the t-spanner as an approximation of the complete graph of distances among the objects, and use it as a compact device to simulate the large matrix of distances required by successful search algorithms like AESA [Vidal 1986]. The t-spanner provides a time-space tradeoff where full AESA is just one extreme. We show that the resulting algorithm is competitive against current approaches, e.g., 1.5 times the time cost of AESA using only 3.21% of its space requirement, in a metric space of strings; and 1.09 times the time cost of AESA using only 3.83 % of its space requirement, in a metric space of documents. We also show that t-spanners provide better space-time tradeoffs than classical alternatives such as pivot-based indexes. Furthermore, we show that the concept of t-spanners has potential for large improvements.