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Maximizing Bisubmodular and kSubmodular Functions
"... 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 ..."
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and bisubmodular functions corresponding to k = 1 and 2, respectively. In this paper, we consider the problem of maximizing bisubmodular and, more generally, ksubmodular functions in the value oracle model. We provide the first approximation guarantees for maximizing a general bisubmodular or ksubmodular
Bisubmodular Function Minimization
 Mathematical Programming
, 2000
"... This paper presents the rst combinatorial, polynomialtime algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. A bisubmodular function arises as a rank function of a deltamatroid. The scali ..."
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Cited by 51 (4 self)
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This paper presents the rst combinatorial, polynomialtime algorithm for minimizing bisubmodular functions, extending the scaling algorithm for submodular function minimization due to Iwata, Fleischer, and Fujishige. A bisubmodular function arises as a rank function of a delta
A MinMax Theorem for ksubmodular Functions and Extreme Points of the Associated Polyhedra
, 2013
"... A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of ksubmodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions. They presented a minmax relation for the ksubmodular function minimization by considering ℓ1 norm, which requires a nonconvex ..."
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A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of ksubmodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions. They presented a minmax relation for the ksubmodular function minimization by considering ℓ1 norm, which requires a non
Balanced Bisubmodular Systems and Bidirected Flows
, 1996
"... For a nonempty finite set V let 3 V be the set of all the ordered pairs of disjoint subsets of V , i.e., 3 V = f(X; Y ) j X; Y ` V; X " Y = ;g. We define two operations, reduced union t and intersection u, on 3 V as follows: for each (X i ; Y i ) 2 3 V (i = 1; 2) (X1 ; Y1) t (X2 ; Y2 ..."
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2 ) = ((X1 [ X2 ) \Gamma (Y1 [ Y2 ); (Y1 [ Y2) \Gamma (X1 [ X2 )); (X1 ; Y1) u (X2 ; Y2 ) = (X1 " X2 ; Y1 " Y2): Also, for a ft; ugclosed family F ` 3 V a function f : F ! R is called bisubmodular if for each (X i ; Y i ) 2 F (i = 1; 2) we have f(X1 ; Y1) + f(X2 ; Y2) f((X1 ; Y1
Deltamatroids, Jump Systems and Bisubmodular Polyhedra
, 1993
"... We relate an axiomatic generalization of matroids, called a jump system, to polyhedra arising from bisubmodular functions. Unlike the case for usual submodularity, the points of interest are not all the integral points in the relevant polyhedron, but form a subset of them. However, we do show that t ..."
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We relate an axiomatic generalization of matroids, called a jump system, to polyhedra arising from bisubmodular functions. Unlike the case for usual submodularity, the points of interest are not all the integral points in the relevant polyhedron, but form a subset of them. However, we do show
A MINMAX THEOREM FOR TRANSVERSAL SUBMODULAR FUNCTIONS AND ITS IMPLICATIONS∗
"... Abstract. Huber and Kolmogorov [Towards minimizing ksubmodular functions, in Proceedings ..."
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Abstract. Huber and Kolmogorov [Towards minimizing ksubmodular functions, in Proceedings
Generalized Skew Bisubmodularity: A Characterization and a MinMax Theorem
, 2013
"... Huber, Krokhin, and Powell (Proc. SODA2013) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the threevalue domain. In this paper we consider a natural generalization of the c ..."
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Cited by 4 (0 self)
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of the concept of skew bisubmodularity and show a connection between the generalized skew bisubmodularity and a convex extension over rectangles. We also analyze the dual polyhedra, called skew bisubmodular polyhedra, associated with generalized skew bisubmodular functions and derive a minmax theorem
A MinMax . . . Functions and Its Implications
, 2013
"... A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of ksubmodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions and obtained a minmax theorem for minimization of ksubmodular functions. Also F. Kuivinen (2011) considered submodular function ..."
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A. Huber and V. Kolmogorov (ISCO 2012) introduced a concept of ksubmodular function as a generalization of ordinary submodular (set) functions and bisubmodular functions and obtained a minmax theorem for minimization of ksubmodular functions. Also F. Kuivinen (2011) considered submodular
Characterizing a valuated deltamatroid as a family of deltamatroids, Report No
 95849OR, Forschungsinstitut für Diskrete Mathematik, Universität
, 1995
"... Abstract Two characterizations are given for a valuated deltamatroid. Let ( V, 3) be an even deltamatroid on a finite set V with the family 3 of feasible sets. I t is shown that a function S: T+ R is a valuation of (V, 3) if and only if, for each linear weighting p: V Ã ‘ R, the maximizers of S ..."
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Abstract Two characterizations are given for a valuated deltamatroid. Let ( V, 3) be an even deltamatroid on a finite set V with the family 3 of feasible sets. I t is shown that a function S: T+ R is a valuation of (V, 3) if and only if, for each linear weighting p: V Ã ‘ R, the maximizers
Results 1  10
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42