4,670 research outputs found
A Model of Optimal Network Structure for Decentralized Nearest Neighbor Search
One of the approaches for the nearest neighbor search problem is to build a
network which nodes correspond to the given set of indexed objects. In this
case the search of the closest object can be thought as a search of a node in a
network. A procedure in a network is called decentralized if it uses only local
information about visited nodes and its neighbors. Networks, which structure
allows efficient performing the nearest neighbour search by a decentralised
search procedure started from any node, are of particular interest especially
for pure distributed systems. Several algorithms that construct such networks
have been proposed in literature. However, the following questions arise: "Are
there network models in which decentralised search can be performed faster?";
"What are the optimal networks for the decentralised search?"; "What are their
properties?". In this paper we partially give answers to these questions. We
propose a mathematical programming model for the problem of determining an
optimal network structure for decentralized nearest neighbor search. We have
found an exact solution for a regular lattice of size 4x4 and heuristic
solutions for sizes from 5x5 to 7x7. As a distance function we use L1 , L2 and
L_inf metrics. We hope that our results and the proposed model will initiate
study of optimal network structures for decentralised nearest neighbour search
HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces
Nearest neighbor searching of large databases in high-dimensional spaces is
inherently difficult due to the curse of dimensionality. A flavor of
approximation is, therefore, necessary to practically solve the problem of
nearest neighbor search. In this paper, we propose a novel yet simple indexing
scheme, HD-Index, to solve the problem of approximate k-nearest neighbor
queries in massive high-dimensional databases. HD-Index consists of a set of
novel hierarchical structures called RDB-trees built on Hilbert keys of
database objects. The leaves of the RDB-trees store distances of database
objects to reference objects, thereby allowing efficient pruning using distance
filters. In addition to triangular inequality, we also use Ptolemaic inequality
to produce better lower bounds. Experiments on massive (up to billion scale)
high-dimensional (up to 1000+) datasets show that HD-Index is effective,
efficient, and scalable.Comment: PVLDB 11(8):906-919, 201
- …