This question is regarding centralized computation vs. distributed computation. Meaning, performing a calculation on one single processor, or performing it on several processors. I'm looking for an idea (a paper maybe?) that deals with computing the value of a function in a distributed manner.
I will demonstrate my question using an example: consider some function $f\colon\mathbb{R}^n\to\mathbb{R}$, where the value of each of the coordinates is given by a different processor. If, for example, the explicit function is given by $f\left(x\right)=x_1x_2\cdot\ldots\cdot x_n$, then the value $f\left(x\right)$ can only be calculated in a centralized manner, since each processor has to "broadcast" its value to all other processors. Unfortunately, one central processor is not always available.
My question is, are there any papers/work regarding distributed function value calculation? or even estimation? I'm having a hard time to find some relevant work, so any help would be much appreciated.