Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Randomized algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Introduction to algorithms
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Discrete Applied Mathematics - Submodularity
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
0(\sqrt {\log n)} Approximation to SPARSEST CUT in Õ(n2) Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Greedy splitting algorithms for approximating multiway partition problems
Mathematical Programming: Series A and B
Network design for information networks
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for prize collecting forest problems with submodular penalty functions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Submodular function minimization
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 hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
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 simple combinatorial algorithm for submodular function minimization
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
Facility location with hierarchical facility costs
ACM Transactions on Algorithms (TALG)
Symmetry and Approximability of Submodular Maximization Problems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Submodular Function Minimization under Covering Constraints
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
Eagle-eyed elephant: split-oriented indexing in Hadoop
Proceedings of the 16th International Conference on Extending Database Technology
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We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load balancing or minimum-makespan scheduling, submodular sparsest cut and submodular balanced cut, which generalize their respective graph cut problems, as well as submodular function minimization with a cardinality lower bound. We establish upper and lower bounds for the approximability of these problems with a polynomial number of queries to a function-value oracle. The approximation guarantees that most of our algorithms achieve are of the order of $\sqrt{{n}/{\ln n}}$. We show that this is the inherent difficulty of the problems by proving matching lower bounds. We also give an improved lower bound for the problem of approximating a monotone submodular function everywhere. In addition, we present an algorithm for approximating submodular functions with a special structure, whose guarantee is close to the lower bound. Although quite restrictive, the class of functions with this structure includes the ones that are used for lower bounds both by us and in previous work.