Time complexity of memory allocation

Question

What is the time complexity of dynamic memory allocation using new, malloc, etc.? I know very little about how memory allocators are implemented, but I assume the answer is that it depends on the implementation. Therefore, please answer for some of the more common cases/implementations.

Edit: I vaguely remember hearing that heap allocation is unbounded in the worst case, but I'm really interested in the average/typical case.

Answer 1

One of the things you have to realise when dealing with O notation is that it is often very important to understand what n is. If the n is something related to something you can control (eg: the number of elements in a list you want sorted) then it makes sense to look hard at it.

In most heap implementations, your n is the number of contiguous chunks of memory the manager is handling. This is decidedly not something typically under client control. The only n the client really has control over is the size of the chunk of memory she wants. Often this bears no relation to the amount of time the allocator takes. A large n could be as quickly allocated as a small n, or it might take much longer, or it might even be unservicable. All this could change for the same n depending on how previous allocations and deallocations from other clients came in. So really, unless you are implementing a heap, then the proper answer is that it is non-deterministic.

This is why hard realtime programmers try to avoid dynamic allocation (after startup).