if you want O(log(n)) time for accessing values, you will need both a representation of the map and a representation of the inverse map.
otherwise the best you can do is O(log(n)) in one direction and O(n) in the other.
Edit: not O(log(n)), thanks Claudiu, but you are still going to need two data structures to implement the quick access times. And this will be more or less the same space as a dict and an inverse dict.
