Totally tight Chv"atal-Gomory cuts

Let P := {x ∈ R n : Ax 6 b} be a polyhedron and PI its integral hull. A Chv atal-Gomory (CG) cut is a valid inequality for PI of the form (� T A)x 6 � � T b� , with � ∈ R m ;� T A ∈ Z n andT bZ. 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 (� T A)x ∗ = � T b .S uch aC G cut is violated by as much as possible under the assumption that x ∗ ∈ P. c � 2002 Elsevier Science B.V. All rights reserved.