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M-fuzzifying submodular functions
Journal of Intelligent & Fuzzy Systems, 2014In this paper, the concept of M-fuzzifying submodular functions is introduced, which is a generalization of submodular functions in matroid theory. It is shown that M-fuzzifying matroids can be generated from an M-fuzzifying submodular function in different ways.
Xiu, Zhen-Yu, Shi, Fu-Gui
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On submodular function minimization
Combinatorica, 1985zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Submodular Functions and Matroids
2015This chapter presents definitions, relevant properties, and examples of submodular functions, which will be built on in subsequent sections. Techniques for constructing submodular functions and proving submodularity are described. The concept of a matroid, which generalizes the concept of matrix rank, is introduced. The matroid rank, basis, and closure
Andrew Clark +3 more
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Minimizing symmetric submodular functions
Mathematical Programming, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Chapter 9 Submodular Functions
1997Publisher Summary In combinatorial mathematics, submodular functions are a relatively recent phenomenon. Submodular functions can be regarded as a generalization of matroid rank functions. The study of basic subinodular operations, such as convolution and Dilworth truncation is significant for practical algorithm designers because in addition to ...
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Submodular functions and convexity
1983In “continuous” optimization convex functions play a central role. Besides elementary tools like differentiation, various methods for finding the minimum of a convex function constitute the main body of nonlinear optimization. But even linear programming may be viewed as the optimization of very special (linear) objective functions over very special ...
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Submodular Function Minimization under a Submodular Set Covering Constraint
2011In this paper, we consider the problem of minimizing a submodular function under a submodular set covering constraint. We propose an approximation algorithm for this problem by extending the algorithm of Iwata and Nagano [FOCS'09] for the set cover problem with a submodular cost function.
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MATROIDS AND SUBMODULAR FUNCTIONS
The Quarterly Journal of Mathematics, 1976openaire +2 more sources