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Binary Clutter Inequalities for Integer Programs
 Mathematical Programming
, 2003
"... 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 ..."
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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...
Ideal Clutters
, 2001
"... The Operations Research model known as the Set Covering Problem has a wide range of applications. See for example the survey by Ceria, Nobili and Sassano in Annotated Bibliographies in Combinatorial Optimization edited by Dell'Amico, Maoli and Martello [16]. Sometimes, due to the special str ..."
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The Operations Research model known as the Set Covering Problem has a wide range of applications. See for example the survey by Ceria, Nobili and Sassano in Annotated Bibliographies in Combinatorial Optimization edited by Dell'Amico, Maoli and Martello [16]. Sometimes, due to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution that is integer, thus solving the problem. Under which conditions do such integrality properties hold? This question is of both theoretical and practical interest. On the theoretical side, polyhedral combinatorics and graph theory come together in this rich area of discrete mathematics. In this tutorial, we present the state of the art and open problems on this question.
Integer Polyhedra: Combinatorial Properties and Complexity
, 2001
"... A polyhedron having vertices is called integer if all of its vertices are integer. This property is coNPcomplete in general. Recognizing integral setpacking polyhedra is one of the biggest challenges of graph theory (perfectness test). Various other special cases are major problems of discrete ..."
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A polyhedron having vertices is called integer if all of its vertices are integer. This property is coNPcomplete in general. Recognizing integral setpacking polyhedra is one of the biggest challenges of graph theory (perfectness test). Various other special cases are major problems of discrete mathematics.