Oracle Tractability of Skew Bisubmodular
نویسندگان
چکیده
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.
منابع مشابه
Polynomial Combinatorial Algorithms for Skew-bisubmodular Function Minimization
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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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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