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Primal separation algorithms

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>10/2003
<mark>Journal</mark>4OR: A Quarterly Journal of Operations Research
Issue number3
Number of pages16
Pages (from-to)209-224
Publication StatusPublished
<mark>Original language</mark>English


Given an integer polyhedron P ⊂ R^n, an integer point x in P, and a point x* in R^n \ P, the primal separation problem is the problem of finding a linear inequality which is valid for P, violated by x*, and satisfied at equality by x. The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for several well known classes of inequalities for various important combinatorial optimization problems, including the knapsack, stable set and travelling salesman problems.