We consider the problem of nearest-neighbor searching among a set of stochastic sites, where a stochastic site is a tuple (si,⇡i) consisting of a point si in a d-dimensional space and a probability ⇡i determining its existence. The problem is interesting and non-trivial even in 1-dimension, where the Most Likely Voronoi Diagram (LVD) is shown to have worst-case complexity ⌦(n). We then show tha...

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set of point sites S in a static simple polygon P . Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q ∈ P . All distances are measured using the geodesic distance, that is, the length of the shortest path...

Let w ∈ N and U = {0, 1, . . . , 2−1} be a bounded universe of w-bit integers. We present a dynamic data structure for predecessor searching in U . Our structure needs O(log log∆) time for queries and O(log log∆) expected time for updates, where∆ is the difference between the query element and its nearest neighbor in the structure. Our data structure requires linear space. This improves a resul...

Nowadays, Nearest Neighbor Search becomes more and more important when facing the challenge of big data. Traditionally, to solve this problem, researchers mainly focus on building effective data structures such as hierarchical k-means tree or using hashing methods to accelerate the query process. In this paper, we propose a novel unified approximate nearest neighbor search scheme to combine the...

Proximity searching consists in retrieving from a database, objects that are close to a query. For this type of searching problem, the most general model is the metric space, where proximity is defined in terms of a distance function. A solution for this problem consists in building an offline index to quickly satisfy online queries. The ultimate goal is to use as few distance computations as p...

Nearest Neighbor Searching, i.e. determining from a set S of n sites in the plane the one that is closest to a given query point q, is a classical problem in computational geometry. Fast theoretical solutions are known, e.g. point location in the Voronoi Diagram of S, or specialized structures such as so-called Delaunay hierarchies. However, practitioners tend to deem these solutions as too com...

The κ-Nearest Neighbors ( κNN) query is an important spatial query in mobile sensor networks. In this work we extend κNN to include a distance constraint, calling it a l-distant κ-nearest-neighbors (l-κNN) query, which finds the κ sensor nodes nearest to a query point that are also at or greater distance from each other. The query results indicate the objects nearest to the area of interest tha...

Dissimilarity measures, the basis of similarity-based retrieval, can be viewed as a distance and a similarity-based search as a nearest neighbor search. Though there has been extensive research on data structures and search methods to support nearest-neighbor searching, these indexing and dimension-reduction methods are generally not applicable to non-coordinate data and non-Euclidean distance ...

Dimension reduction is a highly useful tool in algorithm design, with applications in nearest neighbor searching, clustering, streaming, sketching, learning, approximation algorithms, vision and others. It removes redundancy from data and can be plugged into algorithms suffering from a ”curse of dimensionality”. In my talk, I will describe a novel technique for reducing the dimension of points ...

A novel approach for k-nearest neighbor (k-NN) searching with Euclidean metric is described. It is well known that many sophisticated algorithms cannot beat the brute-force algorithm when the dimensionality is high. In this study, a probably correct approach, in which the correct set of k-nearest neighbors is obtained in high probability, is proposed for greatly reducing the searching time. We ...