Research output: Working paper
Research output: Working paper
}
TY - UNPB
T1 - Binary clutter inequalities for integer programs
AU - Letchford, A N
N1 - This was eventually published as: A.N. Letchford (2003) Binary clutter inequalities for integer programs. Math. Program., 98(1-3), 201-221.
PY - 2002
Y1 - 2002
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 Travelling 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 Travelling 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 - travelling salesman problem
M3 - Working paper
T3 - Management Science Working Paper Series
BT - Binary clutter inequalities for integer programs
PB - The Department of Management Science
CY - Lancaster University
ER -