Closest pair for any of a huge number of points

Question

We are given a huge set of points in 2D plane. We need to find, for each point the closest point within the set. For instance suppose the initial set is as follows:

 foo <- data.frame(x=c(1,2,4,4,10),y=c(1,2,4,4,10))

The output should be like this:

 ClosesPair(foo)
 2
 1
 4
 3
 3 # (could be 4 also)

Any idea?

Answer 1

The traditional approach is to preprocess the data and put it in a data structure, often a K-d tree, for which the "nearest point" query is very fast.

There is an implementation in the nnclust package.

library(nnclust)
foo <- cbind(x=c(1,2,4,4,10),y=c(1,2,4,4,10))
i <- nnfind(foo)$neighbour
plot(foo)
arrows( foo[,1], foo[,2], foo[i,1], foo[i,2] )

Answer 2

Here is an example; all wrapped into a single function. You might want to split it a bit for optimization.

ClosesPair <- function(foo) {
  dist <- function(i, j) {
    sqrt((foo[i,1]-foo[j,1])**2 + (foo[i,2]-foo[j,2])**2)
  }

  foo <- as.matrix(foo)

  ClosestPoint <- function(i) {  
    indices <- 1:nrow(foo)
    indices <- indices[-i]

    distances <- sapply(indices, dist, i=i, USE.NAMES=TRUE)

    closest <- indices[which.min(distances)]
  }

  sapply(1:nrow(foo), ClosestPoint)
}
ClosesPair(foo)
# [1] 2 1 4 3 3

Of cause, it does not handle ties very well.

Answer 3

Use the package spatstat . It's got builtin functions to do this sort of stuff.