Data structure for non-overlapping ranges within a single dimension

Question

I need a data structure that can store non-overlapping ranges within a single dimension. The entire range of the dimension need not be completely covered.

An example

Answer 1

This is non-trivial because (in the database world) you have to compare multiple rows to determine non-overlapping ranges. Clearly, when the information is in memory, then other representations such as lists in time order are possible. I think, though, that you'd be best off with your 'start + end' notation, even in a list.

There are whole books on the subject - part of 'Temporal Database' handling. Two you could look at are Darwen, Date and Lorentzos "Temporal Data and the Relational Model" and (at a radically different extreme) "Developing Time-Oriented Database Applications in SQL", Richard T. Snodgrass, Morgan Kaufmann Publishers, Inc., San Francisco, July, 1999, 504+xxiii pages, ISBN 1-55860-436-7. That is out of print but available as PDF on his web site at cs.arizona.edu (so a Google search makes it pretty easy to find).

One of the relevant data structures is, I believe, an R-Tree. That is often used for 2-dimensional structures, but can also be effective for 1-dimensional structures.

You can also look for "Allen's Relations" for intervals - they may be helpful to you.