Overview

The Cookie Cutter problem behind Project 2 is clearly non-trivial and computationally intense. While this problem does not exhibit an obvious optimal substructure, we theorize that an approximate partitioning of the problem into simpler ones might bring us closer to a solution. Furthermore, we hypothesize that approximating the optimal cookie placement could be done without the extensive loop iterations employed by other groups. Ultimately, we sought a Cookie Cutter design that would be both speedy and near correct.

We broke the Cookie Cutter problem into a number of subproblems. First, we considered the problem of optimally fitting together the copies of a cookie shape. Second, once an appropriate grouping of cookie copies has been arranged, we focussed our efforts on making the cluster of cookie copies conform to the restrictions placed upon the cookie dough dimensions. Third, in a parallel fashion, we broke the domain of cookies into convex and concave shapes. Hopefully, these subproblems would be more manageable than the problem of placing each copy of each cookie template.

Besides simplifying the overall problem, we also did not want to rely upon the CPU to do what some mathematics could probably calculate in constant time. For example, computing the optimal rotation of a copy of a cookie to fit with its counterparts could be done without iterating through the discrete divisions of the range of $360\,^{\circ}$. Since we are merely trying to tile a shape, we believe that there should be a measurable relationship between a cookie's shape, its corners, and its edges. Estimating this relationship should allow our player to make fewer rotations and translations to arrive at a near optimal solution.

``Famous Frugal Amos,'' (FFA) the submitted implementation of our Cookie Cutter player, met limited success when pitted against the likes of the formidable ``Pillsbury Doughboy,'' its cousin, ``Modified Pillsbury Doughboy,'' and the deceptively named, ``Dumb and Dumber.'' With the completion of some modules integral to our overall strategy, we would have signically enhanced our performance.