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An analysis of approximations for maximizing submodular set functions—I

Mathematical Programming, 1978
LetN be a finite set andz be a real-valued function defined on the set of subsets ofN that satisfies z(S)+z(T)źz(SźT)+z(SźT) for allS, T inN. Such a function is called submodular. We consider the problem maxSźN{a(S):|S|≤K,z(S) submodular}. Several hard combinatorial optimization problems can be posed in this framework.
Nemhauser, G. L.   +2 more
openaire   +2 more sources

Rigid Network Design Via Submodular Set Function Optimization

IEEE Transactions on Network Science and Engineering, 2015
We consider the problem of constructing networks that exhibit desirable algebraic rigidity properties, which can provide significant performance improvements for associated formation shape control and localization tasks. We show that the network design problem can be formulated as a submodular set function optimization problem and propose greedy ...
Iman Shames, Tyler H. Summers
openaire   +2 more sources

Submodular Function Minimization with Submodular Set Covering Constraints and Precedence Constraints

Workshop on Approximation and Online Algorithms, 2018
In this paper, we consider the submodular function minimization problem with submodular set covering constraints and precedence constraints, and we prove that the algorithm of McCormick, Peis, Verschae, and Wierz for the precedence constrained covering problem can be generalized to our setting.
Naoyuki Kamiyama
openaire   +2 more sources

Best Algorithms for Approximating the Maximum of a Submodular Set Function

Mathematics of Operations Research, 1978
A real-valued function z whose domain is all of the subsets of N = {1, …, n) is said to be submodular if z(S) + z(T) ≥ z(S ∪ T) + z(S ∩ T), ∀S, T ⊆ N, and nondecreasing if z(S) ≤ z(T), ∀S ⊂ T ⊆ N. We consider the problem maxS⊂N {z(S): |S| ≤ K, z submodular and nondecreasing, z(Ø) = 0}.
Nemhauser, G. L., Wolsey, L. A.
openaire   +3 more sources

Rough set methods in feature selection via submodular function

Soft Computing, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhu, Xiao-Zhong   +2 more
openaire   +3 more sources

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