We can think of the class $NC$ as the class of problems that can be solved in parallel, whereas a $P$-complete problem probably has no parallel solution. My question is: where do online algorithms fit in this spectrum?
My intuition says that online problems are more difficult than parallel problems. This would be more-or-less confirmed by the existence of an online algorithm for a $P$-complete problem. So do any exist?
Alternatively, we could define a complexity class for online problems $O$ such that: $$ NC \subseteq O \subseteq P $$ Then we would have to define $O$-complete problems and convince ourselves that they cannot be parallelized.
Any advice on what I should read to think about this some more?