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Binary clutter inequalities for integer programs

Research output: Working paper

Published

Publication date2002
Place of publicationLancaster University
PublisherThe Department of Management Science
Number of pages0
Original languageEnglish

Publication series

NameManagement Science Working Paper Series

Abstract

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.

Bibliographic note

This was eventually published as: A.N. Letchford (2003) Binary clutter inequalities for integer programs. Math. Program., 98(1-3), 201-221.