Quick Streaming Algorithms for Maximization of Monotone Submodular Functions in Linear Time

• URL: http://arxiv.org/abs/2009.04979v3
• Date: Mon, 8 Mar 2021 17:49:18 GMT
• Title: Quick Streaming Algorithms for Maximization of Monotone Submodular Functions in Linear Time
• Authors: Alan Kuhnle
• Abstract summary: We consider the problem of monotone, submodular over a ground set of size $n$ subject to cardinality constraint $k$. We introduce the first deterministic algorithms with linear time complexity; these algorithms are streaming algorithms. Our single-pass algorithm obtains a constant ratio in $lceil n / c rceil + c$ oracle queries, for any $c ge 1$.
• Score: 16.346069386394703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these algorithms are streaming algorithms. Our single-pass algorithm obtains a constant ratio in $\lceil n / c \rceil + c$ oracle queries, for any $c \ge 1$. In addition, we propose a deterministic, multi-pass streaming algorithm with a constant number of passes that achieves nearly the optimal ratio with linear query and time complexities. We prove a lower bound that implies no constant-factor approximation exists using $o(n)$ queries, even if queries to infeasible sets are allowed. An empirical analysis demonstrates that our algorithms require fewer queries (often substantially less than $n$) yet still achieve better objective value than the current state-of-the-art algorithms, including single-pass, multi-pass, and non-streaming algorithms.

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