Streaming Algorithms for Submodular Function Maximization

Abstract

We consider the problem of maximizing a nonnegative submodular set function $f:2^{\mathcal{N}}\to {\mathbb{R}}^{+}$ 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 {\em non-monotone}. We describe deterministic and randomized algorithms that obtain a $\Omega (\frac{1}{p})$-approximation using $O(k\log k)$-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.

29 pages, 7 figures, extended abstract to appear in ICALP 2015