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Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints
, 2013
"... We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of realworld appl ..."
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Cited by 14 (8 self)
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We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real
Fast algorithms for maximizing submodular functions
 In SODA
, 2014
"... There has been much progress recently on improved approximations for problems involving submodular objective functions, and many interesting techniques have been developed. However, the resulting algorithms are often slow and impractical. In this paper we develop algorithms that match the best know ..."
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Cited by 13 (3 self)
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time. Our first result is a simple algorithm that gives a (1 − 1/e − )approximation for a cardinality constraint using O(n log n ) queries, and a 1/(p + 2 ` + 1 + )approximation for the intersection of a psystem and ` knapsack (linear) constraints using O ( n2 log 2 n ) queries. This is the first
THE SUBMODULAR KNAPSACK POLYTOPE
 FORTHCOMING IN DISCRETE OPTIMIZATION
, 2009
"... The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 01 knapsack set. One motivation for studying the submodular knapsack polytope is to address 01 programming problems with uncertain coefficients. Under various as ..."
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Cited by 1 (1 self)
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The submodular knapsack set is the discrete lower level set of a submodular function. The modular case reduces to the classical linear 01 knapsack set. One motivation for studying the submodular knapsack polytope is to address 01 programming problems with uncertain coefficients. Under various
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 40 (1 self)
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monotone submodular functions. In particular, for any constant k, we present a 1 k+2+ 1 k +ǫapproximation for the submodular maximization problem under k matroid constraints, 1 k+ǫ and a ( 1 5 − ǫ)approximation algorithm for this problem subject to k knapsack constraints (ǫ> 0 is 1 any constant). We improve
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 146 (18 self)
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functions is NPhard. In this paper, we design the first constantfactor approximation algorithms for maximizing nonnegative submodular functions. In particular, we give a deterministic local search 1 2approximation and a randomizedapproximation algo
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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subject to d knapsack constraints, where d is a fixed constant. We establish a strong relation between the discrete problem and its continuous relaxation, obtained through extension by expectation of the submodular function. Formally, we show that, for any nonnegative submodular function, an α
Zeroforcing methods for downlink spatial multiplexing in multiuser MIMO channels
 IEEE TRANS. SIGNAL PROCESSING
, 2004
"... The use of spacedivision multiple access (SDMA) in the downlink of a multiuser multipleinput, multipleoutput (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the coc ..."
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Cited by 371 (29 self)
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channel interference of other users. Typical optimization problems of interest include the capacity problem—maximizing the sum information rate subject to a power constraint—or the power control problem—minimizing transmitted power such that a certain qualityofservice metric for each user is met. Neither
Nearoptimal sensor placements in gaussian processes
 In ICML
, 2005
"... When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in t ..."
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Cited by 342 (34 self)
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information is NPcomplete. To address this issue, we describe a polynomialtime approximation that is within (1 − 1/e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We
Submodular Maximization with Cardinality Constraints
, 2014
"... We consider the problem of maximizing a (nonmonotone) submodular function subject to a cardinality constraint. In addition to capturing wellknown combinatorial optimization problems, e.g., MaxkCoverage and MaxBisection, this problem has applications in other more practical settings such as natu ..."
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Cited by 16 (2 self)
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We consider the problem of maximizing a (nonmonotone) submodular function subject to a cardinality constraint. In addition to capturing wellknown combinatorial optimization problems, e.g., MaxkCoverage and MaxBisection, this problem has applications in other more practical settings
Results 1  10
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