Balanced 0, ±1 Matrices Part I. Decomposition
نویسندگان
چکیده
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.
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 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 کاملColorings of k-balanced matrices and integer decomposition property of related polyhedra
We show that a class of polyhedra, arising from certain 0, 1 matrices introduced by Truemper and Chandrasekaran, has the integer decomposition property. This is accomplished by proving certain coloring properties of these 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 کاملRecognizing Balanceable Matrices
A 0/ ± 1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4. A 0/1 matrix is balanceable if its nonzero entries can be signed ±1 so that the resulting matrix is balanced. A signing algorithm due to Camion shows that the problems of recognizing balanced 0/ ± 1 matrices and balanceable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000