Function input to output size relationship. What is it? Any notable research on it?
I think it's improper to call this measure 'complexity'. A more apt name would be 'input to output size relation'.

Note that, strictly speaking, this is a property of the problem you are solving, not of the particular algorithm you use to solve the problem.

In the case of the compression problem, if you mean lossless compression of arbitrary binary data, then the average compression ratio is never less than 1 (and it's typically strictly greater than 1).