Integer and combinatorial optimization
Integer and combinatorial optimization
The Boolean quadric polytope: some characteristics, facets and relatives
Mathematical Programming: Series A and B
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In this note, we consider the problem of maximizing an arbitrary Boolean polynomial of degree n. We ''linearize'' the problem and give a complete linear description of the resulting polytope. By examining the dual of the corresponding linear program, we find that the problem of maximizing an arbitrary set function defined on the set \s{1,...,n\s} is in one-to-one correspondence with our problem. Moreover, a known result concerning the polynomial solvability of quadratic Boolean functions is generalized to arbitrary Boolean polynomials.