TY - JOUR

T1 - Binary clutter inequalities for integer programs

AU - Letchford, A N

PY - 2003

Y1 - 2003

N2 - We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the {0, 1/2}-cuts of Caprara and Fischetti as a special case and have some interesting connections to binary matroids, binary clutters and Gomory corner polyhedra. We show that the separation problem for BC-cuts is strongly NP-hard in general, but polynomially solvable in certain special cases. As a by-product we also obtain new conditions under which {0, 1/2}-cuts can be separated in polynomial time. These ideas are then illustrated using the Traveling Salesman Problem (TSP) as an example. This leads to an interesting link between the TSP and two apparently unrelated problems, the T -join and max-cut problems.

AB - We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the {0, 1/2}-cuts of Caprara and Fischetti as a special case and have some interesting connections to binary matroids, binary clutters and Gomory corner polyhedra. We show that the separation problem for BC-cuts is strongly NP-hard in general, but polynomially solvable in certain special cases. As a by-product we also obtain new conditions under which {0, 1/2}-cuts can be separated in polynomial time. These ideas are then illustrated using the Traveling Salesman Problem (TSP) as an example. This leads to an interesting link between the TSP and two apparently unrelated problems, the T -join and max-cut problems.

KW - integer programming

KW - cutting planes

KW - matroid theory

KW - binary clutters

KW - traveling salesman problem

U2 - 10.1007/s10107-003-0402-x

DO - 10.1007/s10107-003-0402-x

M3 - Journal article

VL - 98

SP - 201

EP - 221

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-3

ER -