Comment by gsliepen

That would indeed satisfy std::map, but then the question is, is that a useful ordering for intervals? To answer that, you need to define what you want to use the interval map for. If you want to be able to lookup in which unique interval a given value is, then you shouldn't have overlapping intervals to begin with. If you do allow overlapping intervals, a query could result in multiple intervals. Are lookups by value (not by interval) still O(log N) with that ordering?