
LinearTime Algorithms for Adaptive Submodular Maximization
In this paper, we develop fast algorithms for two stochastic submodular ...
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Regularized Nonmonotone Submodular Maximization
In this paper, we present a thorough study of maximizing a regularized n...
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Nearly LinearTime, Parallelizable Algorithms for NonMonotone Submodular Maximization
We study parallelizable algorithms for maximization of a submodular func...
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Fast Adaptive NonMonotone Submodular Maximization Subject to a Knapsack Constraint
Constrained submodular maximization problems encompass a wide variety of...
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Fast Evolutionary Algorithms for Maximization of CardinalityConstrained Weakly Submodular Functions
We study the monotone, weakly submodular maximization problem (WSM), whi...
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Submodular Maximization through the Lens of Linear Programming
The simplex algorithm for linear programming is based on the fact that a...
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Stochastic Conditional Gradient++
In this paper, we develop Stochastic Continuous Greedy++ (SCG++), the fi...
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Beyond Pointwise Submodularity: NonMonotone Adaptive Submodular Maximization in Linear Time
In this paper, we study the nonmonotone adaptive submodular maximization problem subject to a cardinality constraint. We first revisit the adaptive random greedy algorithm proposed in <cit.>, where they show that this algorithm achieves a 1/e approximation ratio if the objective function is adaptive submodular and pointwise submodular. It is not clear whether the same guarantee holds under adaptive submodularity (without resorting to pointwise submodularity) or not. Our first contribution is to show that the adaptive random greedy algorithm achieves a 1/e approximation ratio under adaptive submodularity. One limitation of the adaptive random greedy algorithm is that it requires O(n× k) value oracle queries, where n is the size of the ground set and k is the cardinality constraint. Our second contribution is to develop the first lineartime algorithm for the nonmonotone adaptive submodular maximization problem. Our algorithm achieves a 1/eϵ approximation ratio (this bound is improved to 11/eϵ for monotone case), using only O(nϵ^2logϵ^1) value oracle queries. Notably, O(nϵ^2logϵ^1) is independent of the cardinality constraint.
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