How to find optimal partition subsets Given a partition $[0,1]$，there are 5000 partition subsets $P_i=[a_{i1},a_{i2}]\in[0,1], 0≤a_{i1}\leq a_{i2} \leq 1, i \in \{1,2,...,5000\}$. I want to analyze these subsets and find 10 subsets to contain sixty or seventy percent of the subsets. These 10 subsets could be disjoint, or even overlapping.
First, let me be sure u r aware of SET PACKING &amp; SET PARTITIONING Problems  

https://slideplayer.com/slide/4514539/

Then, I think ur problem is much easier avoiding the overlapping &amp; the complete coverage constraints.

Going simple, here r some heuristics (think as u solving for max/optimal accepting 30%-40%"deviation from optimality) 

1-Pick the max. length partition, then in the next 9th steps choose bet the global max of remaining partitions &amp; the max of those starting after what u have reached so far.... I think that's O(10*5000) let's call it $ O(k n) $

2-Do something similar to $Bucket$ $Sorting$ 

Divide the partition to 10 smaller partitions(put an overlapping sub partition in its starting point bucket) , then select the max length one in each bucket. Still the same order complexity $ O(k*n) $

Finally, maybe a little bit complicated, but if u want a Theoretical abstraction of ur problem I've just watched this about the $maximum$ $K$ $coverage$ problem and the $Influence$ $maximization$ problem.

If u looked to the interval [0,1] as say M smaller/unit sub intervals being ur target population, and viewed each sub partition as connected to/infleuncing the sub intervals(units) it covers. Then u want to select $K$ (10 in ur case) subpartitions that gives u maximum coverage/influence

https://youtu.be/GqKbx3LCQqE