Bisubmodular Function Minimization
نویسندگان
چکیده
This paper presents the first combinatorial polynomial algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. Since the rank functions of delta-matroids are bisubmodular, the scaling algorithm naturally leads to the first combinatorial polynomial algorithm for testing membership in delta-matroid polyhedra.
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-...
متن کاملSubmodularity on a Tree: Unifying $L^\natural$ -Convex and Bisubmodular Functions
We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions f satisfying f(x) + f(y) ≥ f(x ⊓ y) + f(x ⊔ y) where the domain of each variable xi corresponds to nodes of a rooted binary tree, and operations ⊓,⊔ are defined with respect to this tree. Special cases include previously studied L-convex and bisubmodular functions, which...
متن کاملOracle Tractability of Skew Bisubmodular
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.
متن کاملTitle Generalized skew bisubmodularity: A characterization and a min‒max theorem
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. In this paper we consider a natural generalization of the concept of skew bisubmodularity and show a connection between the generalized skew bisubmodularity and a con...
متن کاملOn Bisubmodular Maximization
Bisubmodularity extends the concept of submodularity to set functions with two arguments. We show how bisubmodular maximization leads to richer value-of-information problems, using examples in sensor placement and feature selection. We present the first constant-factor approximation algorithm for a wide class of bisubmodular maximizations.
متن کامل