[davidcuddeback]

"Nearest gap" doesn't sounds like a range query to me. It sounds more like a nearest neighbor query. It sounds like you have (start time, duration) tuples and want to search for nearest neighbor on start time with an at-least-X constraint on duration. (start time, duration) is more point-like than interval-like (as far as data structures go), so anything that can handle nearest neighbor on point-like data would be a candidate. If this is an accurate mapping for your problem, you might check out KD trees. You'd probably have to write a custom tree traversal algorithm to query NN on one dimension and >X on the other, but I think it could be done. Sounds kinda fun.

[grovesNL]

I have (start time, duration) tuples but would like to find the nearest entries (in either direction) given a specific time and minimum duration.

Thanks for the suggestion! I've tried some other spatial acceleration structures (e.g., R-tree and some others) and applying them in 1-d but they didn't outperform the ordered map unfortunately. It could be interesting to try out KD trees at some point though.

[davidcuddeback]

Sure thing! I'd reframe this as a nearest neighbor search over (start time, duration) tuples. KD trees are what I'm most familiar with for that problem, but there are others that would fit. Check out chapters 1 ("Multidimensional Point Data") and 3 ("Intervals and Small Rectangles") of Foundations of Multidimensional and Metric Data Structures: https://books.google.com/books?id=vO-NRRKHG84C&pg=PR9&source...

R-trees are more generic in that they can store intervals, shapes, volumes, etc, but (start time, duration) tuples are point-like, and that opens more possibilities. The ordered map is going to give you good memory locality. It might be that you'll only beat that when searching for larger durations (that require you to iterate over more of your ordered map). There will probably be an inflection point somewhere, depending on the distribution of your data and queries.

Hope that helps!