# Function input to output size relationship. What is it? Any notable research on it?

I'm working on a problem and I've come to a point where I need to define the input/output complexity of an algorithm. I don't remember ever studying this systematically like I did time complexity or space complexity, so what are some notable papers that deal with this problem?

Note: I'm calling it input/output complexity, but I have no idea what the actual name of this is, that would be helpful to know too! Incase it's unclear I am calling the relationship between a functions input and it's output, "Input/Output Complexity"

Examples:

• F({1,2,3,4}) = {1,2} //where the relationship is n/2
• F(some 20 byte input) = 2bytes of header + 10bytes of output //the relationship is 2+n/2
• F(2 byte header + 10byte data) = 6 bytes output // n3/5 - 2

A more concrete example would finding be the average and best input/output complexity of a compression algorithm

Defining this is out of scope of my paper so I am hoping to find a definition/solution to reference.