منابع مشابه
On Nearest-Neighbor Graphs
The “nearest neighbor” relation, or more generally the “k nearest neighbors” relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper, we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on t...
متن کاملNearest-Neighbor Graphs
Consider a set of points that are independently and uniformly distributed in the -dimensional unit cube. Let ∈ . There exists almost-surely ∈ such that 6= and | − | | − | for all ∈ , 6= , 6= . The point is called the nearest neighbor of and we write ≺ . Note that ≺ does not imply ≺ . Draw an edge connecting and if and only if ≺ ; the resulti...
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Large probabilistic graphs arise in various domains spanning from social networks to biological and communication networks. An important query in these graphs is the k nearestneighbor query, which involves finding and reporting the k closest nodes to a specific node. This query assumes the existence of a measure of the “proximity” or the “distance” between any two nodes in the graph. To that en...
متن کاملThe Diameter of Nearest Neighbor Graphs
Any connected plane nearest neighbor graph has diameter Ω(n). This bound generalizes to Ω(n) in any dimension d. For any set of n points in the plane, we define the nearest neighbor graph by selecting a unique nearest neighbor for each point, and adding an edge between each point and its neighbor. This is a directed graph with outdegree one; thus it is a pseudo-forest. Each component of the pse...
متن کاملCluster Identification in Nearest-Neighbor Graphs
Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are “identified”: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1997
ISSN: 0179-5376,1432-0444
DOI: 10.1007/pl00009293