What's the name of this packing problem? I'm trying to pack sets of intervals, to find distinct buckets of intervals. The buckets should not be overlapping.
For example if I have these intervals:
A: [ [0, 10] ]
B: [ [1, 3], [5, 7] ]
C: [ [8, 10] ]

I want to get the following result:
[0, 1]: [A]
[1, 3]: [A, B]
[3, 5]: [A]
[5, 7]: [A, B]
[7, 8]: [A]
[8, 10]: [A, C]

What's the name of this problem?
The problem can be stated as finding the elementary intervals for a given set of intervals. It is a technique frequently used for problems in computational geometry (as suggested by nir shahar also).