An algorithm for solving the assignment problem that is based on the following version of a theorem that was first stated by the Hungarian mathematician König and later generalized by the Hungarian mathematician Egerváry: if Av is a matrix and m is the maximum number of independent zero elements of A,v then m lines can be drawn in the rows and columns of the matrix that contain all the zero elements of A.v (A set of elements of a matrix is said to be independent if no two elements lie in the same row or column.)