Suppose a CSP has $n$ variables with finite domains of maximal size $d$. Furthermore, all constraints on the variables are binary. Can such a CSP be solved in polynomial time in $n$ and $d$?
This was an exam question on last year’s AI exam, but I’m not sure how to solve it.
I know the problem of graph coloring is easily reduced to such a binary CSP, so solving them is NP-complete. Thus, I’m pretty sure that there is no known polynomial-time algorithm. Can I prove that there isn’t one?