منابع مشابه
Balanced 0-1 Matrices I. Decomposition
A 0, \1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0, 1 matrices obtained by Conforti, Cornue jols, and Rao (1999, J. Combin. Theory Ser. B 77, 292 406) to the class of balanced 0, \1 matrices. As a consequence, we obtain a polynomial time algorithm f...
متن کاملBalanced 0, ±1 Matrices Part I. Decomposition
A 0; 1 matrix is balanced if, in every square submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This paper extends the decomposition of balanced 0; 1 matrices obtained by Conforti, Cornu ejols and Rao to the class of balanced 0; 1 matrices. As a consequence, we obtain a polynomial time algorithm for recognizing balanced 0; 1 matrices.
متن کاملDecomposition of Balanced Matrices
A 0; 1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0,1 matrix is either totally unimodular or its bipartite representation has a cutset consisting of two adjacent nodes and some of their neighbors. This result yields a polytime recognition algorithm for balancedness. To prove the result, we rst prove a d...
متن کاملBalanced 0, ±1 Matrices Part II. Recognition Algorithm
In this paper we give a polynomial time recognition algorithm for balanced 0; 1 matrices. This algorithm is based on a decomposition theorem proved in a companion paper.
متن کامل(0, ±1) Ideal Matrices
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. ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2000.2010