I am not a user of custom allocator, but I was wondering whether a custom allocator can be used to redefine the growing strategy. For example, in most implementations, a std::vector grows geometrically. Would it be possible to change this strategy for an arithmetic growth, like adding 10 elements everytime a reallocation is necessary. And if the answer if yes, then how to do that?
No. The reallocation strategy is defined by vector, not by the allocator it uses. The allocator is there only to provide the memory - it is up to the vector itself to tell it how much memory to provide.
The standard mandates that push_back is amortized constant time. From [vector.modifiers]
Complexity: The complexity is linear in the number of elements inserted plus the distance to the end of the vector.
Since push_back must be O(1), the growth strategy of vector must not be arithmetic - otherwise we'd have linear-time insertion.
To do what you want, you'd have to provide your own vector-like container and implement your own push_back() member function.