This paper introduces a novel type of query, what we name Spatio-temporal Pattern Queries (STP). Such a query specifies a spatio-temporal pattern as a sequence of distinct spatial predicates where the predicate temporal ordering (exact or relative) matters. STP queries can use various types of spatial predicates (range search, nearest neighbor, etc.) where each such predicate is associated (1) ...

Given n data points in d-dimensional space, nearest neighbor searching involves determining the nearest of these data points to a given query point. Most average-case analyses of nearest neighbor searching algorithms are made under the simplifying assumption that d is xed and that n is so large relative to d that boundary eeects can be ignored. This means that for any query point the statistica...

We modify the k-d tree on [0, 1]d by always cutting the longest edge instead of rotating through the coordinates. This modification makes the expected time behavior of lowerdimensional partial match queries behave as perfectly balanced complete k-d trees on n nodes. This is in contrast to a result of Flajolet and Puech [J. Assoc. Comput. Mach., 33 (1986), pp. 371–407], who proved that for (stan...

In this paper, we develop a general framework for approximate nearest neighbor queries. We categorize the current approaches for nearest neighbor query processing based on either their ability to reduce the data set that needs to be examined, or their ability to reduce the representation size of each data object. We first propose modifications to wellknown techniques to support the progressive ...

Given a set S of points in a metric space with distance function D, the nearest-neighbor searching problem is to build a data structure for S so that for an input query point q, the point s ∈ S that minimizes D(s, q) can be found quickly. We survey approaches to this problem, and its relation to concepts of metric space dimension. Several measures of dimension can be estimated using nearest-nei...

in this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. the nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. the results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant effect...

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...

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 two. Since the exact nearest neighbor search problem suffers from the curse of dimension...

Little work has been reported in the literature to support k-nearest neighbor (k-NN) searches/ queries in hybrid data spaces (HDS). An HDS is composed of a combination of continuous and non-ordered discrete dimensions. This combination presents new challenges in data organization and search ordering. In this paper, we present an algorithm for k-NN searches using a stages and use the properties ...