Let $A$ be a set of $n$ closed intervals, $I_i$, with both extremes positive integers. Is there an efficient algorithm to find a set of $n$ points $P_i$, with $P_i \in I_i$, such that the minimum distance between all pairs of points is maximized?
Assume that the intervals are bounded by a positive integer $C$.
What's the complexity of this problem?
If the intervals are non-overlapping, I know how to solve this with linear programming (indeed, using a system of difference constraints and Bellman-Ford), but what can we say about the general case where intervals might overlap?
Note: Most comments/answers so far are looking for a polynomial solution. Note that it is possible that this problem is NP-complete. I know that it was the style of this teacher to include problems for which students had to prove NP-completeness.