An accelerated sequential algorithm for producing D-optimal designs
SIAM Journal on Scientific and Statistical Computing
Randomized algorithms
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
An 0.828–approximation algorithm for the uncapacitated facility location problem
Discrete Applied Mathematics
The Data-Correcting Algorithm for the Minimization of Supermodular Functions
Management Science
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Combinatorial approximation algorithms for the maximum directed cut problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Some optimal inapproximability results
Journal of the ACM (JACM)
A 0.5-Approximation Algorithm for MAX DICUT with Given Sizes of Parts
SIAM Journal on Discrete Mathematics
Non-oblivious Local Search for MAX 2-CCSP with Application to MAX DICUT
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Constrained Maximum-Entropy Sampling
Operations Research
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
On the complexity of approximating k-set packing
Computational Complexity
Solving maximum-entropy sampling problems using factored masks
Mathematical Programming: Series A and B
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Optimal marketing strategies over social networks
Proceedings of the 17th international conference on World Wide Web
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
Proceedings of the 9th ACM conference on Electronic commerce
The Journal of Machine Learning Research
Encouraging Cooperation in Sharing Supermodular Costs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Evolutionary Algorithms and Matroid Optimization Problems
Algorithmica - Including a Special Section on Genetic and Evolutionary Computation; Guest Editors: Benjamin Doerr, Frank Neumann and Ingo Wegener
Symmetry and Approximability of Submodular Maximization Problems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
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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. Unlike submodular minimization, submodular maximization is NP-hard. In this paper, we give the first constant-factor approximation algorithm for maximizing any nonnegative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for nonmonotone submodular functions. In particular, for any constant $k$, we present a $(\frac{1}{k+2+\frac{1}{k}+\epsilon})$-approximation for the submodular maximization problem under $k$ matroid constraints, and a $(\frac{1}{5}-\epsilon)$-approximation algorithm for this problem subject to $k$ knapsack constraints ($\epsilon0$ is any constant). We improve the approximation guarantee of our algorithm to $\frac{1}{k+1+\frac{1}{k-1}+\epsilon}$ for $k\geq2$ partition matroid constraints. This idea also gives a $(\frac{1}{k+\epsilon})$-approximation for maximizing a monotone submodular function subject to $k\geq2$ partition matroids, which is an improvement over the previously best known guarantee of $\frac{1}{k+1}$.