Decomposition methods work by grouping variables into sets, and solving a subproblem for each set. Presently environmentalism is focused on solving the proper coupling subproblem. The problem being solved is split into two problems&colon; the master problem and the subproblem. Considering a different subproblem in each step. This information is then utilized in the objective function of the subproblem. The base case is the trivial subproblem, which occurs for a board. Then, for each subproblem "i", it performs the following steps. The subproblem is a new problem created to identify a new variable. In subproblem "i", let "V" denote the set of remaining variables. Eventually, one reaches a subproblem size that fits into cache, regardless of the cache size.