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Balanced 0, ±1-matrices, bicoloring and total dual integrality (1995)

Conforti, Michele ; Cornuéjols, Gérard

Springer

Mathematical programming 71 (1995), S. 249-258

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ISSN: 1436-4646

Keywords: Combinatorial optimization ; Integrality of polyhedra ; Generalized set packing ; Covering

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract A 0, ±1-matrixA is balanced if, in every submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This definition was introduced by Truemper (1978) and generalizes the notion of a balanced 0, 1-matrix introduced by Berge (1970). In this paper, we extend a bicoloring theorem of Berge (1970) and total dual integrality results of Fulkerson, Hoffman and Oppenheim (1974) to balanced 0, ±1-matrices.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01590956

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Testing balancedness and perfection of linear matrices (1993)

Conforti, Michele ; Rao, M. R.

Springer

Mathematical programming 61 (1993), S. 1-18

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ISSN: 1436-4646

Keywords: Combinatorial optimization ; (0, 1) matrices ; integrality of polyhedra

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract A (0, 1) matrix is linear if it does not contain a 2×2 submatrix of all ones. In this paper we give polynomial algorithms to test whether a linear matrix is balanced or perfect. The algorithms are based on decomposition results previously obtained by the authors.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01582135

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A Theorem of Truemper (2000)

Conforti, Michele ; Gerards, Bert ; Kapoor, Ajai

Springer

Combinatorica 20 (2000), S. 15-26

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ISSN: 1439-6912

Keywords: AMS Subject Classification (1991) Classes: 05C50, 05B35

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s004930070028

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