Efficient algorithm for grouping points in clusters by the distance between every two points

Question

I am looking for an efficient algorithm for the following problem:

Given the many points in 2D space, where each point is determined by its X and Y coordinates. It is required to split this set of points into a set of clusters, so if the distance between two arbitrary points is less than a certain threshold, these points must belong to one cluster:

In other words, such a cluster is a set of points that are fairly close to each other.

A naive algorithm might look like this:

• Let R be the resulting list of clusters, initially empty
• Let P be a list of points, initially contains all points
• P C, . P
• Pi P 4. Pc C 4AA. (Pi, Pc) < , Pi C P
• ​​ C 4, 4
• C R. P , 3

. , ?

P.S. apriori

Answer 1

:

• DBSCAN

.

Answer 2

• . , threshhold/sqrt (8).

• P, , , . , , (). sqaures S.

• S c. c S. .

• , sqaures, C. 3 S. S , .