How can we assume comparison, addition, … between numbers is $O(1)$
When we calculate the time-complexity of some algorithm we make many simplifications (or assumptions) on our calculation. For instance we say that assume basic arithmetic operations are all constant time and we assume reading/writing to a memory location is constant time.
I've worked on some algorithms where these assumptions don't hold. I'm looking for the background I need to properly approach/describe these algorithms. In particular I wish to know:
- What is the generic name for such a simplification/assumption?
- Is there a name for the basic model of simplifications we're using? (Assuming there is a common model)
Note: I've done work with cache-dependent/cache-oblivious algorithms. I understand how to calculate in that domain, but I'm lacking the terminology/background to properly compare/contrast such algorithm analyis with that which don't consider the cache.