DeepAI AI Chat
Log In Sign Up

Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity

by   Georgios Amanatidis, et al.

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 adaptive complexity, capturing the number of sequential rounds of parallel computation needed. In this work we obtain the first constant factor approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with 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 Õ(n^2) value queries, but can be modified to run with only Õ(n) instead, while retaining a low adaptive complexity of O(log^2n). Besides the above improvement in adaptivity, this is also the first 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.


page 1

page 2

page 3

page 4


An Optimal Approximation for Submodular Maximization under a Matroid Constraint in the Adaptive Complexity Model

In this paper we study submodular maximization under a matroid constrain...

Nearly Linear-Time, Parallelizable Algorithms for Non-Monotone Submodular Maximization

We study parallelizable algorithms for maximization of a submodular func...

A polynomial lower bound on adaptive complexity of submodular maximization

In large-data applications, it is desirable to design algorithms with a ...

DASH: Distributed Adaptive Sequencing Heuristic for Submodular Maximization

The development of parallelizable algorithms for monotone, submodular ma...

Linear Query Approximation Algorithms for Non-monotone Submodular Maximization under Knapsack Constraint

This work, for the first time, introduces two constant factor approximat...

Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint

Constrained submodular maximization problems encompass a wide variety of...

Submodular Maximization Subject to Matroid Intersection on the Fly

Despite a surge of interest in submodular maximization in the data strea...