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Dettaglio pubblicazione

2021, Proceedings of the 38th International Conference on Machine Learning, Pages 231-242 (volume: 139)

Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity (04b Atto di convegno in volume)

Amanatidis Georgios, Fusco Federico, Lazos Filippos, Leonardi Stefano, Marchetti-Spaccamela Alberto, 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 $ ilde{O}(n^2)$ value queries, but can be modified to run with only $ ilde{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.
Gruppo di ricerca: Algorithms and Data Science
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