A Unified Approach to Approximate Proximity Searching
نویسندگان
چکیده
The inability to answer proximity queries efficiently for spaces of dimension d > 2 has led to the study of approximation to proximity problems. Several techniques have been proposed to address different approximate proximity problems. In this paper, we present a new and unified approach to proximity searching, which provides efficient solutions for several problems: spherical range queries, idempotent spherical range queries, spherical emptiness queries, and nearest neighbor queries. In contrast to previous data structures, our approach is simple and easy to analyze, providing a clear picture of how to exploit the particular characteristics of each of these problems. Despite the simplicity and generality of our data structures, our complexities essentially match the most efficient data structures known and often offer small improvements. As applications of our approach, we provide simple and practical data structures that match the best previous results up to logarithmic factors, as well as advanced data structures that improve over the best previous results for all aforementioned proximity problems.
منابع مشابه
A numerical approach for variable-order fractional unified chaotic systems with time-delay
This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...
متن کاملDiameter Approximate Best Proximity Pair in Fuzzy Normed Spaces
The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...
متن کاملProximity Searching in High Dimensional Spaces with a Proximity Preserving Order
Kernel based methods (such as k-nearest neighbors classifiers) for AI tasks translate the classification problem into a proximity search problem, in a space that is usually very high dimensional. Unfortunately, no proximity search algorithm does well in high dimensions. An alternative to overcome this problem is the use of approximate and probabilistic algorithms, which trade time for accuracy....
متن کاملExistence of common best proximity points of generalized $S$-proximal contractions
In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...
متن کاملApproximate String Matching ? Edgar
We present a radically new indexing approach for approximate string matching. The scheme uses the metric properties of the edit distance and can be applied to any other metric between strings. We build a metric space where the sites are the nodes of the suux tree of the text, and the approximate query is seen as a proximity query on that metric space. This permits us nding the R occurrences of ...
متن کامل