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Cones of alternating and cut submodular set functions
Combinatorica, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Submodular function minimization and polarity
Mathematical programming, 2019Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; hence, it is equivalent to the Lovász extension.
Alper Atamtürk, Vishnu Narayanan
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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 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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A fast double greedy algorithm for non-monotone DR-submodular function maximization
Discret. Math. Algorithms Appl., 2019We study the problem of maximizing non-monotone diminish return (DR)-submodular function on the bounded integer lattice, which is a generalization of submodular set function.
Shuyang Gu +3 more
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Multi-Pass Streaming Algorithms for Monotone Submodular Function Maximization
Theory of Computing Systems, 2018We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to only a small ...
Chien-Chung Huang, Naonori Kakimura
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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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Convex Analysis for Minimizing and Learning Submodular Set Functions
2013The 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, 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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On Submodular Set Cover Problems for Near-Optimal Online Kernel Basis Selection
IEEE International Conference on Acoustics, Speech, and Signal Processing, 2022Hrusikesha Pradhan +2 more
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