I observed that all the interval tree implementations I am able to come up with are required to utilize a stack (or a-like) to answer queries (report any overlapping interval with a key).
In general when visiting a node in an (common) interval tree you are required to visit multiple child nodes and check for results there and recurse. This requires you to (dynamically) allocate memory upon lookup.
In contrast, f.e. consider a simple binary search tree. You can easily unroll the recursion because you will only ever visit a single child node.
Is it possible to achieve a similar algorithm for intervals? To clarify I would like to know whether there exists an interval tree which supports finding any overlapping interval in constant required space.