{0, 1/2}-Chvátal-Gomory cuts

Given the integer polyhedronPt:= conv{x ∈ℤn:Ax⩽b}, whereA ∈ℤm × n andb ∈ℤm, aChvátal-Gomory (CG)cut is a valid inequality forP1 of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ+m such that λτA∈ℤn . In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2}m. We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of strong inequalities forP1. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering polytopes are briefly discussed.