is a matrix with the preference order of all individuals in the market. If there are n individuals, then this matrix will be of dimension n by n. The i,jth element refers to j's ith most favorite partner. Preference orders must be specified using C++ indexing (starting at 0).

is a vector of length n corresponding to the matchings being made, so that e.g. if the 4th element is 5 then agent 4 was matched to agent 6. This vector uses C++ indexing that starts at 0.