There is no standard container which gives such guarantees out from the box, some additional manipulation are required (for instance, like Jerry Coffin suggested), it is NOT duplicate.
Are there any ready data structure/container with at least O(ln N) on random access and O(ln N) on delete? (stl/boost/etc)
Ordering of elements within container is not important.
Such operations may happen in series, like:
random access by index ( index is random too, rand()%size() )
delete this item
random access by index ( index is random too, rand()%size() )
delete this item
etc...