I faced a problem that looks very hard, the problem is this:
We have 5 people putting dots on a whiteboard, each person uses colored dots with a different color (there are 5 colors, 1 for each person). My job is to find a cluster of points which contains 3 or more distinct colors. Also, we have some fixed radius $R$, and the distance for each point in a given cluster shouldn't be more than R. Also, there might be points that don't belong to any cluster.
What kind of approach can you suggest? At first, I tried the Multidimensional linear assignment problem, but it seems that this problem is NP-hard, so I want to solve it in a reasonable amount of time (I write code). What kind of solutions can you suggest? Maybe using the fact that this isn't a general problem, I mean we use 2D space where people take action, also there are only 5 people.