The design and analysis of spatial data structures
The design and analysis of spatial data structures
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Multidimensional binary search trees used for associative searching
Communications of the ACM
Item-based collaborative filtering recommendation algorithms
Proceedings of the 10th international conference on World Wide Web
ACM Computing Surveys (CSUR)
Similarity Search in High Dimensions via Hashing
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Searching in Metric Spaces by Spatial Approximation
SPIRE '99 Proceedings of the String Processing and Information Retrieval Symposium & International Workshop on Groupware
Mercury: supporting scalable multi-attribute range queries
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
One torus to rule them all: multi-dimensional queries in P2P systems
Proceedings of the 7th International Workshop on the Web and Databases: colocated with ACM SIGMOD/PODS 2004
Fast Approximate Similarity Search in Extremely High-Dimensional Data Sets
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
M-Chord: a scalable distributed similarity search structure
InfoScale '06 Proceedings of the 1st international conference on Scalable information systems
Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Effective Proximity Retrieval by Ordering Permutations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distributed similarity search in high dimensions using locality sensitive hashing
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Peer to peer multidimensional overlays: approximating complex structures
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Similarity grid for searching in metric spaces
DELOS'04 Proceedings of the 6th Thematic conference on Peer-to-Peer, Grid, and Service-Orientation in Digital Library Architectures
Nearest neighbor pattern classification
IEEE Transactions on Information Theory
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We propose a novel approach for solving the approximate nearest neighbor search problem in arbitrary metric spaces. The distinctive feature of our approach is that we can incrementally build a non-hierarchical distributed structure for given metric space data with a logarithmic complexity scaling on the size of the structure and adjustable accuracy probabilistic nearest neighbor queries. The structure is based on a small world graph with vertices corresponding to the stored elements, edges for links between them and the greedy algorithm as base algorithm for searching. Both search and addition algorithms require only local information from the structure. The performed simulation for data in the Euclidian space shows that the structure built using the proposed algorithm has navigable small world properties with logarithmic search complexity at fixed accuracy and has weak (power law) scalability with the dimensionality of the stored data.