I've been learning about NP-Complete problems, and came across the rectangle fit problem. Basically, the rectangle-fit problem is the problem of whether or not a set of 2d rectangles can fit in a larger 2d rectangle. What I have not been able to find, or solve myself, is what a possible solution looks like.
Say there is a set of rectangles $R$ and a large rectangle $T$, how do I indicate a possible placement of all rectangles in $R$ into $T$? I was thinking coordinates, but there is no assumption $T$ is defined as a graph. At a high level, how would I denote where/how each rectangle should be placed?
I am not asking for how to solve this NP-Complete problem. I am asking how do I define the placement of rectangles in $R$ for a candidate solution. I saw an academic paper saying that it is obvious there is a polynomial time verifier for the problem, but there was no explanation of what the certificate the verifier is using looks like.
Particularly, I was looking at: http://ranger.uta.edu/~weems/NOTES5311/hw3ansold.pdf for the verifier.