Totally tight Chvátal-Gomory cuts

Let P := {x∈Rn: Ax6 b} be a polyhedron and PI its integral hull. A Chv atal–Gomory (CG) cut is a valid inequality for PI of the form ( A)x6 b , with ∈R+; TA∈ Z and b ∈ Z . We give a polynomial-time algorithm which, given some x∗ ∈P, detects whether a totally tight CG cut exists, i.e., whether there is a CG cut such that ( TA)x∗= b. Such a CG cut is violated by as much as possible under the assumption that x∗ ∈P. c © 2002 Elsevier Science B.V. All rights reserved.