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Binary clutter inequalities for integer programs

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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.

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  1. Department of Management Science, Lancaster University, Lancaster, LA1 4YW, England

    Adam N. Letchford

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  1. Adam N. Letchford
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Correspondence to Adam N. Letchford.

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Mathematics Subject Classification: 90C10

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Letchford, A. Binary clutter inequalities for integer programs. Math. Program., Ser. B 98, 201–221 (2003). https://doi.org/10.1007/s10107-003-0402-x

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  • DOI: https://doi.org/10.1007/s10107-003-0402-x

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