Map between two sets of points that minimizes their total distance

Question

Let's have a set of $N$ points at positions $\vec{R}_i$, where $i=1...N$. They are displaced into arbitrary positions $\vec{r}_{M(i)}$, where $M(i)=1...N$. The problem is to find a map $M: i \mapsto M(i)$ such that $S = \sum_{i=1}^N |\vec{r}_{M(i)}-\vec{R}_i|^2$ is a minimum. In other words, we want to renumber the points in the second set such that sum of squares between corresponding points is a minimum. Any idea where to look for a solution of this problem?