need an algorithm for collapsing netblock ranges into lists of superset ranges

Question

My math-fu is failing me! I need an efficient way of reducing network ranges to supersets, e.g. if I input list of IP ranges:

• 1.1.1.1 to 2.2.2.5
• 1.1.1.2 to 2.2.2.4
• 10.5.5.5 to 155.5.5.5
• 10.5.5.6 to 10.5.5.7

I want to return the following ranges:

• 1.1.1.1 to 2.2.2.5
• 10.5.5.5 to 155.5.5.5

Note: the input lists are not ordered (though they could be?). The naive way to do this is to check every range in the list to see if the input range x is a subset, and if so, NOT insert range x. However, whenever you insert a new range it might be a superset of existing ranges, so you have to check the existing ranges to see if they can be collapsed (e.g., removed from my list).

Answer 1

This is a union of segments computation. An optimal algorithm (in O(nlog(n))) consists in doing the following:

2. sort all endpoints (starting and ending points) in a list L (each endpoint should know the segment it belongs to). If an endpoint is equal to a starting point, the starting point should be considered smaller than the enpoint.
3. go through the sorted list L from left to right and maintain the number LE-RE, where LE is the number of left endpoints that you have already passed, and RE is the number of right endpoints that you have already passed.
4. each time LE-RE reaches zero, you are at the end of a connected union of segments, and you know that the union of the segments you have seen before (since the previous return to zero) is one superset.
5. if you also maintained the min and max, between each return to zero, you have the bounds of the superset.

At the end, you obtain a sorted list of disjoint supersets. Still, two supersets A and B can be adjacent (the endpoint of A is just before the starting point of B). If you want A and B to be merged, you can do this either by a simple postprocessing step, or by slightly modifying step 3: when LE-RE reaches zero, you would consider it the end of a superset only if the next element in L is not the direct successor of your current element.

Answer 2

You know that you can easily convert IPv4 addresses to int numbers (int32 numbers), do you? Working with int numbers is much easier. So basically every address is a number in the range 0 to 2^32. Every range has a start number and an end number. Your example

1.1.1.1 to 2.2.2.5
1.1.1.2 to 2.2.2.4

can be written as

16,843,009 to 33,686,021
16,843,010 to 33,686,020

So it's pretty easy to see if one range is within the other range. A range is completely within the other range if the following condition is given

startIP2 >= startIP1 && startIP2 <= endIP1 &&
endIP1 >= startIP1 && endIP2 <= endIP1

In that case the range startIP2-endIP2 is completely within startIP1-endIP1. If only the first line is true, then startIP2 is within the range startIP1-endIP1, but the end is beyond the range. If only the second line is true, the endIP is within the range, but the start IP is beyond the range. In that case, if only one line is true, you need to expand the range at the beginning or at the end. If both lines are false, the ranges are completely disjoint, in that case they are two completely independent ranges.