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Extreme points of a set of contents majorized by a submodular set function
Archiv der Mathematik, 1992The extreme points of the set of contents (finitely additive measures) on an algebra \(\mathcal A\), which are majorized by a submodular set function \(u\), have already been characterized for certain special cases [see \textit{J. Rosenmüller}, Arch. Math. 22, 420-430 (1971; Zbl 0237.28002), \textit{F. Dalbaen}, J. Math. Anal. Appl.
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Maximizing Submodular Set Functions: Formulations and Analysis of Algorithms
1981We consider integer programming formulations of problems that involve the maximization of submodular functions. A location problem and a 0–1 quadratic program are well-known special cases. We give a constraint generation algorithm and a branch-and-bound algorithm that uses linear programming relaxations.
G.L. Nemhauser, L.A. Wolsey
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Matroids and Submodular Functions for Covering-Based Rough Sets
2019Covering-based rough set theory is an extension of Pawlak’s rough set theory, and it was proposed to expand the applications of the latter to more general contexts. In this case a covering is used instead of the partition obtained from an equivalence relation.
Mauricio Restrepo, John Fabio Aguilar
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Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
2007Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider the problem $\max_{S \in \cal I} f(S)$. It is known that the greedy algorithm yields a 1/2-approximation [9] for this problem. It is also known, via a reduction from the max-k-cover problem, that there is no (1 i¾?
Gruia Calinescu +3 more
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Approximation Operators in Covering Based Rough Sets from Submodular Functions
2017We present a new collection of upper approximation operators for covering based rough sets, obtained from sub modular functions and closure operators. Each non decreasing submodular function defines a closure operator that can be considered as an approximation operator. The construction allows us to define several upper approximation operators.
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Accelerated greedy algorithms for maximizing submodular set functions
2005Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E maximizing f over P(E). Many combinatorial optimization problems can be formulated in these terms. Here, a family of approximate solution methods is studied : the greedy algorithms.
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On greedy algorithms, partially ordered sets, and submodular functions
IBM Journal of Research and Development, 2003Brenda L. Dietrich, Alan J. Hoffman
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Submodular set functions and monotone systems in aggregation problems. II
[For part I see Autom. Remote Control 48, No.5, 679-689 (1987; Zbl 0639.90077).] The relationship from part I between submodular functions and functions determining the extremal properties of monotone sytems is applied to prove that, on the chain of any set-theoretical interval, the submodular function varies more slowly than the linear function of theMuchnik, I. B., Shvartser, L. V.
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Submodular Function Minimization and Polarity
Mathematical Programming, 2022Alper Atamtürk, Vishnu Narayanan
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