K-means algorithm variation with equal cluster size

Question

I\'m looking for the fastest algorithm for grouping points on a map into equally sized groups, by distance. The k-means clustering algorithm looks straightforward and promis

Answer 1

In general, grouping points on a map into equally sized groups, by distance is a impossible mission in theory. Because grouping points into equally sized groups is in conflict with grouping points in clusters by distance.

see this plot:

There are four points:

A.[1,1]
B.[1,2]
C.[2,2]
D.[5,5]

If we cluster these points into two cluster. Obviously, (A,B,C) will be cluster 1, D will be cluster 2. But if we need equally sized groups, (A,B) will be one cluster, (C,D) will be the other. This violates cluster rules because C is closer to center of (A,B) but it belongs to cluster (C,D). So requirement of cluster and equally sized groups can not be satisfied at the same time.