t-Spanners for metric space searching
نویسندگان
چکیده
منابع مشابه
t-Spanners for metric space searching
The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a t-spanner G′(V,E) as the representation of the metric database. A t-spanner is a subgraph G′(V,E) of a graph G(V,A), such that E ⊆ A and G′ approximates the s...
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A t-spanner, a subgraph that approximates graph distances within a precision factor t, is a well known concept in graph theory. In this paper we use it in a novel way, namely as a data structure for searching metric spaces. The key idea is to consider the t-spanner as an approximation of the complete graph of distances among the objects, and use it as a compact device to simulate the large matr...
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[Who doesn’t understand a glance, won’t understand a long explanation either.] – Arab proverb The problem of Similarity Searching consists in finding the elements from a set which are similar to a given query under some criterion. If the similarity is expressed by means of a metric, the problem is called Metric Space Searching. In this thesis we present new methodologies to solve this problem u...
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Let G(V,A) be a connected graph with a nonnegative cost function d : A → R. Let dG(u, v) be the cost of the cheapest path between u, v ∈ V . A tspanner of G is a subgraph G(V,E), E ⊆ A, such that ∀ u, v ∈ V, dG′(u, v) ≤ t · dG(u, v), t > 1. We focus on the metric space context, which means that A = V ×V , d is a metric, and t ≤ 2. Several algorithms to build t-spanners are known, but they do no...
متن کاملNearest-Neighbor Searching and Metric Space Dimensions
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...
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ژورنال
عنوان ژورنال: Data & Knowledge Engineering
سال: 2007
ISSN: 0169-023X
DOI: 10.1016/j.datak.2007.05.002