2026-07-25T23:58:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12665 2024-03-06T10:51:23Z ddc:004 open_access

Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints Huang, Chien-Chung Thiery, Theophile Ward, Justin submodular maximization streaming algorithms matroid matchoid 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(p³klog(k)/ε³) elements gives a (p+1+γ+O(ε))-approximation, where γ is the guarantee of the best-known offline algorithm for the same problem. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Chien-Chung Huang and Theophile Thiery and Justin Ward 2020 Is Part Of LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2020.62 urn:nbn:de:0030-drops-126657 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.62 eng https://creativecommons.org/licenses/by/3.0/legalcode