I'm currently working on a problem that I came across:
You are given a set $B$ of $n$ points in the plane, and a set $R$ of $n$ points in the plane. Each point is given by its coordinates. I have to Suggest an $O(n^{3})$ time algorithm for determining if there is a perfect matching between them, with the constraint that each point in $R$ is matched to a point in $B$ point whose distance is at most 1 unit away.
I have tried solving using the minimum distance using bipartite algorithm but could not arrive at a solution. Can anyone provide me with any ideas?