G. Cornuejols, Combinatorial Optimization: Packing and Covering, CBMS-NSF Regional Conference Series in Applied Mathematics 74, SIAM (2001).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....2 R m be defined by letting i (A) be the numberofentries in row i of A that are equal to ;1. Following others, 10 a0# Sigma1 matrix is ideal if the fractional generalizedcovering polyhedron fx 2 R n : Ax e ; A)# 0 x eg has only integer extreme points. see [9, 31,15], for example) These polyhedra are the natural ones to study when formulating propositional logic problems in conjunctive normal form as linear 0,1 optimization problems (see [8, 38] Let (A) 2 R m be defined by letting i (A) be the number of entries in row i of A that are equal to 1. ....

....that the constraint matrix is not ordinarily totally unimodular. Finally,wewonder whether there is some higher reason that explains why the generalized covering formulations for balanced 0# Sigma1 matrices and for the 11 clipped cubes are totally dual integral. The inductiveproofscheme in [15]for demonstrating the total dual integrality of generalized covering formulations having 0# Sigma1 balanced constraint matrices, relies only on the idealness of the constraint matrix and all submatrices obtained by the deletion of rows. So that proof scheme can be adapted here as well. So ....

G'erard Cornu'ejols. Combinatorial Optimization: Packing and Covering. (manuscript), 1999.

....A, let (A) 2 R m be defined by letting i (A) be the number of entries in row i of A that are equal to Gamma1. Following others, 10 a 0; Sigma1 matrix is ideal if the fractional generalized covering polyhedron fx 2 R n : Ax e Gamma (A) 0 x eg has only integer extreme points. see [9, 31, 15], for example) These polyhedra are the natural ones to study when formulating propositional logic problems in conjunctive normal form as linear 0,1 optimization problems (see [8, 38] Let (A) 2 R m be defined by letting i (A) be the number of entries in row i of A that are equal to 1. ....

....that the constraint matrix is not ordinarily totally unimodular. Finally, we wonder whether there is some higher reason that explains why the generalized covering formulations for balanced 0; Sigma1 matrices and for the 11 clipped cubes are totally dual integral. The inductive proof scheme in [15] for demonstrating the total dual integrality of generalized covering formulations having 0; Sigma1 balanced constraint matrices, relies only on the idealness of the constraint matrix and all submatrices obtained by the deletion of rows. So that proof scheme can be adapted here as well. So ....

G'erard Cornu'ejols. Combinatorial Optimization: Packing and Covering. (manuscript), 1999.

....for which M(C(M) M . The 0,1 matrix M is ideal if the clutter C(M) is ideal. Clearly, C(M) is ideal if and only if fx 0 : Mx 1g is an integral polyhedron. In this tutorial we present the state of the art and open problems on ideal clutters and matrices. Parts of the tutorial overlap with [10]. 2 1.1 Blockers A transversal of a clutter C is a set of vertices that intersects all the edges. The blocker b(C) of a clutter C is the clutter with V (C) as vertex set and the minimal transversals of C as edge set. That is, E(b(C) consists of the minimal members of fB V (C) jB Aj 1 ....

G. Cornuejols, Combinatorial Optimization: Packing and Covering, CBMS-NSF Regional Conference Series in Applied Mathematics 74, SIAM (2001).

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G. Cornuejols, Combinatorial Optimization: Packing and Covering, Regional Conference Series in Applied Mathematics, SIAM 2001.

No context found.

G. Cornuejols, Combinatorial Optimization: Packing and Covering, Regional Conference Series in Applied Mathematics, SIAM 2001.

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