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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
An improved coating pan apparatus and spray arm assembly are disclosed for providing facilitated maintenance and cleaning of sensitive spray nozzles. The spray arm assembly includes means for varying
Optimal approximation for the submodular welfare problem in the value oracle model
  • J. Vondrák
  • Computer Science, Mathematics
    STOC
  • 17 May 2008
TLDR
A randomized continuous greedy algorithm is developed which achieves a (1-1/e)-approximation for the Submodular Welfare Problem in the value oracle model and is shown to have a potential of wider applicability on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.
Fast algorithms for maximizing submodular functions
TLDR
A new variant of the continuous greedy algorithm, which interpolates between the classical greedy algorithm and a truly continuous algorithm, is developed, which can be implemented for matroid and knapsack constraints using O(n2) oracle calls to the objective function.
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
TLDR
The generalized assignment problem (GAP) is a special case of the problem, and although the reduction requires |N| to be exponential in the original problem size, it is able to interpret the recent (1 i¾? 1/e)-approximation for GAP by Fleischer et al.[10] in the framework.
Lazier Than Lazy Greedy
TLDR
The first linear-time algorithm for maximizing a general monotone submodular function subject to a cardinality constraint is developed, and it is shown that the randomized algorithm, STOCHASTIC-GREEDY, can achieve a (1 — 1/e — e) approximation guarantee, in expectation, to the optimum solution in time linear in the size of the data.
Maximizing Non-monotone Submodular Functions
Submodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs, certain constraint satisfaction problems, and maximum facility
Submodular maximization by simulated annealing
TLDR
A new algorithm for submodular maximization which is based on the idea of simulated annealing is proposed and it is proved that this algorithm achieves improved approximation for two problems: a 0.41-approximation for unconstrained submodul maximization, and a0.325-app approximation subject to a matroid independence constraint.
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
TLDR
A new {\em swap rounding} technique which can be applied in a variety of settings including matroids and matroid intersection, while providing Chernoff-type concentration bounds for linear and sub modular functions of the rounded solution is described.
Maximizing Non-Monotone Submodular Functions
Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location
Maximizing Non-Monotone Submodular Functions
Submodular maximization generalizes many important problems including Max Cut in directed/undirected graphs and hypergraphs, certain constraint satisfaction problems and maximum facility location
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