منابع مشابه
On k-Submodular Relaxation
k-submodular functions, introduced by Huber and Kolmogorov, are functions defined on {0, 1, 2, . . . , k}n satisfying certain submodular-type inequalities. k-submodular functions typically arise as relaxations of NP-hard problems, and the relaxations by k-submodular functions play key roles in design of efficient, approximation, or FPT algorithms. Motivated by this, we consider the following pr...
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Submodularity is one of the most important property of combinatorial optimization, and k-submodularity is a generalization of submodularity. Maximization of a k-submodular function is NP-hard, and approximation algorithm has been studied. For monotone k-submodular functions, [Iwata, Tanigawa, and Yoshida 2016] gave k/(2k−1)-approximation algorithm. In this paper, we give a deterministic algorit...
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In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively. In particular we generalize the known Min-Max-Theorem for submodular and bisubmodular functions. This theorem asserts that the minimum of the (bi)submodular function can be found by solving a maximization...
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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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The popular K-means clustering partitions a data set by minimizing a sum-of-squares cost function. A coordinate descend method is then used to nd local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2016
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m101926x