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• W2076534077 abstract "Consider a convex relaxation fˆ of a pseudo-Boolean function f. We say that the relaxation is totally half-integral if fˆ(x) is a polyhedral function with half-integral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi=xj, xi=1−xj, and xi=γ where γ∈{0,1,12} is a constant. A well-known example is the roof duality relaxation for quadratic pseudo-Boolean functions f. We argue that total half-integrality is a natural requirement for generalizations of roof duality to arbitrary pseudo-Boolean functions. Our contributions are as follows. First, we provide a complete characterization of totally half-integral relaxations fˆ by establishing a one-to-one correspondence with bisubmodular functions. Second, we give a new characterization of bisubmodular functions. Finally, we show some relationships between general totally half-integral relaxations and relaxations based on the roof duality. On the conceptual level, our results show that bisubmodular functions provide a natural generalization of the roof duality approach to higher-order terms. This can be viewed as a non-submodular analogue of the fact that submodular functions generalize the s-t minimum cut problem with non-negative weights to higher-order terms." @default.
• W2076534077 created "2016-06-24" @default.
• W2076534077 creator A5021390142 @default.
• W2076534077 date "2012-03-01" @default.
• W2076534077 modified "2023-09-29" @default.
• W2076534077 title "Generalized roof duality and bisubmodular functions" @default.
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• W2076534077 doi "https://doi.org/10.1016/j.dam.2011.10.026" @default.
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