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:

Answer 1

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.