Mathematical Programming

, Volume 98, Issue 1, pp 201–221

Binary clutter inequalities for integer programs

Article

DOI: 10.1007/s10107-003-0402-x

Cite this article as:
Letchford, A. Math. Program., Ser. B (2003) 98: 201. doi:10.1007/s10107-003-0402-x

Abstract.

We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the \({{\{0, \frac{{1}}{{2}}\}}}\)-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 \({{\{0, \frac{{1}}{{2}}\}}}\)-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.

Keywords

Integer programmingcutting planesmatroid theorybinary clutterstraveling salesman problem

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of Management ScienceLancaster UniversityLancasterEngland