Numeric Range Optimization

I have an set numeric ranges that I would like to optimize.

Here's a simple example of initial values:

Start    End
9        12
1        2
60       88
10       11
79       80

What I'd expect as output after optimization:

Start    End
1        2
9        12
60       88

These are the left and right values from Modified Preorder Tree Traversal (Nested Set) data stored in a MySQL database. I use them to exclude inactive branches from the result, and am not currently optimizing the ranges at all. I thought I might get a performance gain from optimizing the ranges before use.

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MORE INFO

The values are passed into a query for exclusion of the inactive branches in the tree using a NOT BETWEEN clause. I thought that I could optimize the performance of that query by using a minimal set of ranges.

Here is an SQL that will return what you want

mysql> CREATE TABLE sample (Start INT, End INT);

mysql> INSERT sample VALUES (9,12),(1,2),(60,88),(10,11),(79,80);

mysql> SELECT * 
    -> FROM sample s 
    -> WHERE NOT EXISTS (SELECT 1 
    ->                   FROM sample 
    ->                   WHERE s.Start > Start AND s.Start < End);
+-------+------+
| Start | End  |
+-------+------+
|     9 |   12 |
|     1 |    2 |
|    60 |   88 |
+-------+------+

You can, of course, create VIEW, move the data to another table or delete rows using the above SQL.

NOTE: I am not really sure why are you doing this 'optimization'.

EDIT:
The query can be rewritten as

SELECT s.* 
FROM sample s LEFT JOIN 
     sample s2 ON s.Start > s2.Start AND s.Start < s2.End 
WHERE s2.start IS NULL;

Which will create different execution plan (2xsimple select vs primary/dependent subquery for EXISTS), so performance might be different. Both queries will use an index on (Start, End) if it exists.