Interval overlap problem

[psychomike]

Hello,

I am interested in an algorithmic problem, but don't really have a good intuition about its complexity.
So, the problem is as follows:

Given a range of real numbers and given a set of (potentially overlapping and non-connected) sub-regions (= multiple intervals) on this range, what is the minimum set for which its union covers at least a certain amount of the complete range?

As an example, let's assume a number range from 0 to 1 (i.e. [0,1]), and a set of sub-regions with 100 elements could look like this:
1) [0.1,0.2] [0.3,0.35] [0.7,0.9]
2) [0.2,0.4]
3) [0.0,0.05] [0.6,0.85]
4) [0.65,0.8] [0.85,0.95]
5) [0.7,1]
.
.
100) [0.2,0.4]

Each element covers a certain part of the number range, but this part need not be connected.
Now I want to find the minimum subset of elements that cover at least 90% of the original range (assuming this is possible). Elements in this subset may overlap and the final result need not be connected.

I am not sure which complexity class this kind of problem belongs to and if efficient solutions exist.
Can someone help and give me some pointers?

Thanks,

Michael

[Zachm]

This problem is NP-Hard, as there exists a polynomial time reduction from the Set Cover Problem to this problem.

I would try an approximation algorithms approach.

Regards,
Zachm