Results 141 to 150 of about 11,284 (160)

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.
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Cones of alternating and cut submodular set functions

Combinatorica, 1989
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Submodular Function Minimization with Submodular Set Covering Constraints and Precedence Constraints

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.
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Submodular Function Minimization under a Submodular Set Covering Constraint

2011
In 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 for Covering-Based Rough Sets

2019
Covering-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 Submodular Set Functions: Formulations and Analysis of Algorithms

1981
We 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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Multi-level facility location as the maximization of a submodular set function

European Journal of Operational Research, 2015
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Ortiz-Astorquiza, Camilo, Contreras, Ivan, Laporte, Gilbert   +2 more
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Accelerated greedy algorithms for maximizing submodular set functions

2005
Given 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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Convex Analysis for Minimizing and Learning Submodular Set Functions

2013
The connections between convexity and submodularity are explored, for purposes of minimizing and learning submodular set functions. First, we develop a novel method for minimizing a particular class of submodular functions, which can be expressed as a sum of concave functions composed with modular functions.
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Extreme points of a set of contents majorized by a submodular set function

Archiv der Mathematik, 1992
The 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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