Hardness of Approximate Nearest Neighbor Search
نویسنده
چکیده
We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for every δ > 0 there exists a constant ε > 0 such that computing a (1 + ε)-approximation to the Bichromatic Closest Pair requires Ω (
منابع مشابه
Nearest Neighbor Search in Multidimensional Spaces Depth Oral Report
The Nearest Neighbor Search problem is deened as follows: given a set P of n points, preprocess the points so as to eeciently answer queries that require nding the closest point in P to a query point q. If we are willing to settle for a point that is almost as close as the nearest neighbor, then we can relax the problem to the approximate Nearest Neighbor Search. Nearest Neighbor Search (exact ...
متن کاملEFANNA : An Extremely Fast Approximate Nearest Neighbor Search Algorithm Based on kNN Graph
Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the dimensionality of data grows, while hashing based methods usually lack efficiency in practice. Recently, the graph based methods have drawn considerable attention. The ma...
متن کاملNearest Neighbor Search using Kd-trees
We suggest a simple modification to the kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than three. Since the exact nearest neighbor search problem suffers from the curse of dimensi...
متن کاملApproximate nearest neighbor search for $\ell_p$-spaces ($2<p<\infty$) via embeddings
While the problem of approximate nearest neighbor search has been well-studied for Eu-clidean space and ℓ 1 , few non-trivial algorithms are known for ℓ p when 2 < p < ∞. In this paper, we revisit this fundamental problem and present approximate nearest-neighbor search algorithms which give the first non-trivial approximation factor guarantees in this setting.
متن کاملImplementing a Parallel Dynamic Approximate Nearest Neighbor Search Algorithm∗
We describe the implementation of a fast, dynamic, approximate, nearest-neighbor search algorithm that works well in fixed dimensions (d ≤ 5), based on sorting points coordinates in Morton (or z-) ordering. Our code scales well on multi-core/cpu shared memory systems. Our implementation is competitive with the best approximate nearest neighbor searching codes available on the web, especially fo...
متن کامل