(0, ±1) Ideal Matrices
نویسندگان
چکیده
A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of nding a satisfactory characterization of those matrices which are minimally non-ideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally non-ideal matrices. In this paper we consider the extension of the notion of ideality to (0; 1) matrices. By means of a standard transformation, we associate with any (0; 1) matrixA a suitable (0; 1) matrix D(A). Then we introduce the concept of disjoint completion A+ of a (0; 1) matrix A and we show that A is ideal if and only if D(A+) is ideal. Moreover, we introduce a suitable concept of a minimally non-ideal (0; 1) matrix and we prove a Lehman-type characterization of minimally non-ideal (0; 1) matrices. 2
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عنوان ژورنال:
- Math. Program.
دوره 80 شماره
صفحات -
تاریخ انتشار 1995