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Communication Dans Un Congrès Année : 2020

Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints

Chien-Chung Huang
Theophile Thiery
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  • PersonId : 1087946
Justin Ward
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  • PersonId : 1087947

Résumé

We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general p-matchoid constraint in the model in which elements of the ground set arrive one at a time in a stream. The family of constraints we consider generalizes both the intersection of p arbitrary matroid constraints and p-uniform hypergraph matching. For monotone submodular functions, our algorithm attains a guarantee of p + 1 + ε using O(p/ε)-passes and requires storing only O(k) elements, where k is the maximum size of feasible solution. This immediately gives an O(1/ε)-pass (2 + ε)-approximation for monotone submodular maximization in a matroid and (3 + ε)-approximation for monotone submodular matching. Our algorithm is oblivious to the choice ε and can be stopped after any number of passes, delivering the appropriate guarantee. We extend our techniques to obtain the first multi-pass streaming algorithms for general, non-negative submodular functions subject to a p-matchoid constraint. We show that a randomized O(p/ε)-pass algorithm storing O(p3k log (k)/ε3) elements gives a (p + 1 + ̄γoff + O(ε))-approximation, where ̄γoff is the guarantee of the best-known offline algorithm for the same problem
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hal-03099882 , version 1 (06-01-2021)

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  • HAL Id : hal-03099882 , version 1

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Chien-Chung Huang, Theophile Thiery, Justin Ward. Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints. International Conference on Approximation Algorithms for Combinatorial Optimization Problems, Aug 2020, Seattle, United States. ⟨hal-03099882⟩
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