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Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity
Georgios Amanatidis · Federico Fusco · Philip Lazos · Stefano Leonardi · Alberto Marchetti-Spaccamela · Rebecca Reiffenhäuser
The growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the \emph{adaptive complexity}, capturing the number of sequential rounds of parallel computation needed. In this work we obtain the first \emph{constant factor} approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with \emph{near-optimal} $O(\log n)$ adaptive complexity. Low adaptivity by itself, however, is not enough: one needs to account for the total number of function evaluations (or value queries) as well. Our algorithm asks $\tilde{O}(n^2)$ value queries, but can be modified to run with only $\tilde{O}(n)$ instead, while retaining a low adaptive complexity of $O(\log^2n)$. Besides the above improvement in adaptivity, this is also the first \emph{combinatorial} approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. Finally, we showcase our algorithms' applicability on real-world datasets.
Author Information
Georgios Amanatidis (University of Essex)
Federico Fusco (Sapienza University of Rome)
Philip Lazos (Sapienza University of Rome)
Stefano Leonardi (Sapienza University of Rome)
Alberto Marchetti-Spaccamela (Sapienza University of Rome)
Rebecca Reiffenhäuser (Sapienza University of Rome)
Related Events (a corresponding poster, oral, or spotlight)
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2021 Poster: Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity »
Wed. Jul 21st 04:00 -- 06:00 AM Room
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