A special role of Boolean quadratic polytopes among other combinatorial polytopes - Maksimenko, Aleksandr (arXiv.org, 2015)
We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family \(P\) is affinely reduced to a family \(Q\) if for every polytope \(p\in P\) there exists \(q\in Q\) such that \(p\) is affinely equivalent to \(q\) or to a face of \(q\), where \(\dim q = O((\dim p)^k)\) for some constant \(k\). Under this comparison the above-mentioned families are splitted into two equivalence classes. We show also that these two classes are simpler (in the above sence) than the families of poytopes of the following problems: set covering, traveling salesman, 0-1 knapsack problem, 3-satisfiability, cubic subgraph, partial ordering. In particular, Boolean quadratic polytopes appear as faces of polytopes in every of the mentioned families.