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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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A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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On greedy algorithms, partially ordered sets, and submodular functions
IBM Journal of Research and Development, 2003B. L. Dietrich, A. J. Hoffman
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Parallel Quasi-Concave Set Function Optimization for Scalability Even Without Submodularity
2023 IEEE High Performance Extreme Computing Conference (HPEC), 2023Praneeth Vepakomma +3 more
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Maximizing Approximately Non-k-Submodular Monotone Set Function with Matroid Constraint
2022Yanjun Jiang +3 more
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