Properties of balanced and perfect matrices
暂无分享,去创建一个
In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesAI,⋯,An ofA such thatA is balanced if and only if all the submatricesA1,⋯,An ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.
[1] Manfred W. Padberg,et al. Perfect zero–one matrices , 1974, Math. Program..
[2] Michele Conforti,et al. Testing balancedness and perfection of linear matrices , 1993, Math. Program..
[3] Michele Conforti,et al. Articulation sets in linear perfect matrices II: the wheel theorem and clique articulations , 1992, Discret. Math..