Streaming Algorithms for Submodular Function Maximization - Chekuri, Chandra; Gupta, Shalmoli; Quanrud, Kent (Automata, Languages, and Programming, 2015)
We consider the problem of maximizing a nonnegative submodular set function f:2N→R+ $$f:2^{\mathcal {N}} → \mathbb {R}^+$$ subject to a p-matchoid constraint in the single-pass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are non-monotone. We describe deterministic and randomized algorithms that obtain a Ω(1p) $$\varOmega (\frac{1}{p})$$ -approximation using O(klogk) $$O(k \log k)$$ -space, where k is an upper bound on the cardinality of the desired set. The model assumes value oracle access to f and membership oracles for the matroids defining the p-matchoid constraint.