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)
A combinatorial algorithm for minimizing symmetric submodular functions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
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
Evolutionary algorithms and matroid optimization problems
Proceedings of the 9th annual conference on Genetic and evolutionary computation
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
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
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
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
Scheduling to minimize power consumption using submodular functions
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Multi-document summarization via budgeted maximization of submodular functions
HLT '10 Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics
Submodular secretary problem and extensions
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Envy-free pricing with general supply constraints
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
Contact center scheduling with strict resource requirements
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Buyback problem: approximate matroid intersection with cancellation costs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Maximizing Non-monotone Submodular Functions
SIAM Journal on Computing
On the approximability of budget feasible mechanisms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The 1-neighbour knapsack problem
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Optimization with demand oracles
Proceedings of the 13th ACM Conference on Electronic Commerce
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
The knapsack problem with neighbour constraints
Journal of Discrete Algorithms
Matroid and knapsack center problems
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Discovering influential nodes from trust network
Proceedings of the 28th Annual ACM Symposium on Applied Computing
Submodular secretary problem and extensions
ACM Transactions on Algorithms (TALG)
Approximation with a fixed number of solutions of some multiobjective maximization problems
Journal of Discrete Algorithms
SPARSI: partitioning sensitive data amongst multiple adversaries
Proceedings of the VLDB Endowment
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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 non-negative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a (1/k+2+1/k+ε)-approximation for the submodular maximization problem under k matroid constraints, and a (1/5-ε)-approximation algorithm for this problem subject to k knapsack constraints (ε0 is any constant). We improve the approximation guarantee of our algorithm to 1/k+1+{1/k-1}+ε for k≥2 partition matroid constraints. This idea also gives a ({1/k+ε)-approximation for maximizing a monotone submodular function subject to k≥2 partition matroids, which improves over the previously best known guarantee of 1/k+1.