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In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $epsilon$, our algorithm achieves a $1/e - epsilon$ approximation using $O(log{n} log(1/epsilon) / epsilon^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $epsilon$. Previous algorithms achieve worse approximation guarantees using $Omega(log^2{n})$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications in machine
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day applications can
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Profit maximization (PM) is to select a subset of users as seeds for viral marketing in online social networks, which balances between the cost and the profit from influence spread. We extend PM to that under the general marketing strategy, and form