Generalized roof duality
نویسندگان
چکیده
منابع مشابه
Generalized roof duality
The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique ...
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Consider a convex relaxation f̂ of a pseudo-boolean function f . We say that the relaxation is totally half-integral if f̂(x) is a polyhedral function with halfintegral 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 rela...
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We extend the concept of generalized roof duality from pseudo-boolean functions to real-valued functions over multi-label variables. In particular, we prove that an analogue of the persistency property holds for energies of any order with any number of linearly ordered labels. Moreover, we show how the optimal submodular relaxation can be constructed in the first-order case.
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Many problems in computer vision can be turned into a large-scale boolean optimization problem, which is in general NP-hard. In this paper, we further develop one of the most successful approaches, namely roof duality, for approximately solving such problems for higherorder models. Two new methods that can be applied independently or in combination are investigated. The first one is based on co...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.06.009