Given: Set of Set of Intervals. Example {{(1,2), (3,4)}, {(1, 3)}, {(13,14)}}


Wanted Result: Largest Subset, in which no Interval overlaps with another from every Set pairwise.


Example:



```

Input {{(1,2), (3,4)}, {(1, 3)}, {(13,14)}}

A possible Solution would be: {{(1,2), (3,4)}, {(13,14)}}

Another could be {{(1, 3)}, {(13,14)}},
it's not important that the solution above has more 'subelements',
its only important that 2 = |{{(1,2), (3,4)}, {(13,14)}}| = |{{(1, 3)}, {(13,14)}}|

```

Now i am looking for a good/efficient Algorithm to solve that problem.



How to get the largest subset of a set of sets of intervals with no overlapping intervals
Vel Nias gave almost the right answer in:


[How to get the largest subset of a set of sets of intervals with no overlapping intervals](https://mathoverflow.net/questions/98651/how-to-get-the-largest-subset-of-a-set-of-sets-of-intervals-with-no-overlapping-i/98663#98663)


but instead of the connected components we are looking for the maximum independent set in this graph.


