DonnieDarko's blog

How build a graph with points?
By DonnieDarko, history, 6 years ago, In English

If I want to build a graph when the input is a set of points
and an edge exists if the distance between two points is less than
some value x, what is the best way to construct the graph?

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6 years ago, # |
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In the worst case the desired graph will have edges. So you might as well check distance between each pair of points and construct said graph in .

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    6 years ago, # ^ |
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    Thanks man! and in the case that I do not want to build the graph, but put each "component" in a subset, Is there a better approach?

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      6 years ago, # ^ |
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      One (horrible) idea that comes to mind: put the points into square buckets of side . The points within a bucket are clearly linked together. Compute the convex hull in each bucket. Then find the closest distance between the points of a bucket and those of its 12 relevant neighbors with rotating callipers. Link them if that distance is  ≤ x.

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6 years ago, # |
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You could conpute the Delaunay triangulation of the points and then consider only edges which correspont to adjacent faces. This works because the Euclidean MST is known to be a subgraph in this (planar) triangulation graph.

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