3.2. Ordering the border
As in previous algorithms [3,21], we begin by placing the border pieces. First we find the order of the border pieces, then we actually embed the border pieces in the plane.
Each border piece has a right and left side, unambiguously defined by orienting the piece with its straight side down.
In the case of a corner piece, we orient the two straight sides to be down and to the right.
We define a score s(A,B) measuring how well the right side of piece A fits the left side of piece B.
Finding the best ordering is now an asymmetric traveling salesman problem with s(A,B) serving as the distance from “city” A to city B. It is asymmetric in that s(A,B) = s(B,A). We solve this NP-hard problem using the assignment
problem heuristic.