Oracle Tractability of Skew Bisubmodular Functions
نویسندگان
چکیده
منابع مشابه
Oracle Tractability of Skew Bisubmodular Functions
A key task in combinatorial optimisation is the minimisation of discrete functions. Important examples are submodular functions, see e. g. [6, 13, 14, 17], and bisubmodular functions, see e. g. [2, 6, 14, 16]. These functions can be viewed as (special) functions from D to R where D is a 2-element set for the submodular case and a 3-element set for the bisubmodular case. Fix a finite set D. One ...
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In this paper we consider skew bisubmodular functions as recently introduced by the authors and Powell. We construct a convex extension of a skew bisubmodular function which we call Lovász extension in correspondence to the submodular case. We use this extension to show that skew bisubmodular functions given by an oracle can be minimised in polynomial time.
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Huber, Krokhin, and Powell (2013) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the three-value domain, and Huber and Krokhin (2014) showed the oracle tractability of minimization of skew-bisubmodular functions. Fujishige, Tanigawa, and Yoshida (2014) also showed a min-...
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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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Submodular functions play a key role in combinatorial optimization and in the study of valued constraint satisfaction problems. Recently, there has been interest in the class of bisubmodular functions, which assign values to disjoint pairs of sets. Like submodular functions, bisubmodular functions can be minimized exactly in polynomial time and exhibit the property of diminishing returns common...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130936038