Minimum number of sets of points During my work I've encountered this problem:

$G = \{(x_i,y_i,z_i)\}_{i=1}^{n}$ is a group of points in space ($\forall i \;\;  x_i,y_i,z_i \in \Bbb R$) and $ d \in \Bbb R^+$ is a constant.

Divide $G$ to $m$ groups (as few as possible) that follow this rule: for each pair of points in the same group, the distance between these two points is less than or equal to $d$. ($m$ should be, as said, the minimum)

I thought about solving it by turning it into a graph where each point is a node and 2 nodes are connected if and only if the distance between these 2 points is smaller than $d$. Then the solution is the same as finding a minimal cover of the graph using Cliques. This is an NP problem and thus can't be solved in polynomial time unless P=NP. So that doesn't provide a useful solution.

Does anybody have any idea how to solve this problem?
I can't access the paper itself, but judging by its abstract and a mention on p. 5 of this paper, a slight generalisation of your problem was proved NP-hard in 1978: Complete-Link Cluster Analysis by Graph Coloring (Pierre Hansen and Michel Delattre).  I say "slight generalisation" because (I assume that) the problem proved hard allows arbitrary distances between points; it's possible that Euclidean version of the problem, which you seem to have, is easier.  Maybe even the metric version is easier.

For the case of exactly 2 clusters, Wikipedia gives a poly-time algorithm based on 2SAT.