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Maximizing nonmonotone submodular functions
 In Proceedings of 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS
, 2007
"... Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular fu ..."
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Cited by 145 (17 self)
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Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location problems. Unlike the problem of minimizing submodular functions, the problem of maximizing submodular
Maximizing Stochastic Monotone Submodular Functions
"... We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. We study the adaptivity gap the ratio between the values of optimal adaptive and nonadaptive policies and show that it is equal to e. This result implies that the benefit of adaptivi ..."
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Cited by 3 (0 self)
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We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. We study the adaptivity gap the ratio between the values of optimal adaptive and nonadaptive policies and show that it is equal to e. This result implies that the benefit
Maximization of NonMonotone Submodular Functions
"... A litany of questions from a wide variety of scientific disciplines can be cast as nonmonotone submodular maximization problems. Since this class of problems includes maxcut, it is NPhard. Thus, generalpurpose algorithms for the class tend to be approximation algorithms. For unconstrained probl ..."
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A litany of questions from a wide variety of scientific disciplines can be cast as nonmonotone submodular maximization problems. Since this class of problems includes maxcut, it is NPhard. Thus, generalpurpose algorithms for the class tend to be approximation algorithms. For unconstrained
Constrained Maximization of NonMonotone Submodular Functions
, 2009
"... The problem of constrained submodular maximization has long been studied, with nearoptimal results known under a variety of constraints when the submodular function is monotone. The case of nonmonotone submodular maximization is not as well understood: the first approximation algorithms even for un ..."
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The problem of constrained submodular maximization has long been studied, with nearoptimal results known under a variety of constraints when the submodular function is monotone. The case of nonmonotone submodular maximization is not as well understood: the first approximation algorithms even
Nonmonotone submodular maximization under matroid and knapsack constraints
 In Proc. 41th ACM Symp. on Theory of Computing
, 2009
"... Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Un ..."
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Cited by 37 (1 self)
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. Unlike submodular minimization, submodular maximization is NPhard. In this paper, we give the first constantfactor approximation algorithm for maximizing any nonnegative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for nonmonotone
Maximizing a Monotone Submodular Function subject to a Matroid Constraint
, 2008
"... Let f: 2 X → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2 approximation [14] for this problem. For certain special cases, e.g. max S≤k f(S), the greedy algorithm yields a (1 − 1/e)app ..."
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Cited by 63 (0 self)
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Let f: 2 X → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2 approximation [14] for this problem. For certain special cases, e.g. max S≤k f(S), the greedy algorithm yields a (1 − 1/e
Locally Adaptive Optimization: Adaptive Seeding for Monotone Submodular Functions
"... The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objec ..."
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approximation for general monotone submodular functions and circumvents some of the impossibilities associated with nonadaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some
Approximations for Monotone and Nonmonotone Submodular Maximization with Knapsack Constraints
"... Submodular maximization generalizes many fundamental problems in discrete optimization, including MaxCut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we consider the problem of maximizing any submodular function subject ..."
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Cited by 4 (0 self)
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Submodular maximization generalizes many fundamental problems in discrete optimization, including MaxCut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we consider the problem of maximizing any submodular function
Results 1  10
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3,278