Semi-Streaming Algorithms for Submodular Maximization under Random Arrival Order

TL;DR

This paper introduces new semi-streaming algorithms for submodular maximization in random order, improving approximation guarantees and pass complexity for various combinatorial constraints.

Contribution

It presents the first improvements over adversarial order algorithms for many classes, and introduces two technical tools for translating offline algorithms into semi-streaming ones.

Findings

Achieves better approximation ratios for matroids and p-systems in semi-streaming models.

Shows a separation between adversarial and random order algorithms for matroids.

Provides exponential improvements in the number of passes needed for certain constraints.

Abstract

We study random order semi-streaming algorithms for submodular maximization under a wide range of combinatorial constraint classes, including matroids, matroid $p$-parity, $p$-exchange systems and $p$-systems. For most of these classes of constraints, our results are the first improvement over what is known to be achievable for adversarial order. For matroids, matching and $p$-matchoids, previous random order results were known, and we improve over some of these as well. In the case of matroids, our improved results show a separation between adversarial and random order semi-streaming algorithms, and exponentially improve the number of passes necessary for getting $1 - 1/e - \varepsilon$ approximation for maximizing a monotone submodular function subject to a matroid constraint. We also prove a new hardness result showing a similar separation for $p$-systems. Our results are based on two new technical tools. One tool provides a general way to translate offline algorithms for many classes of constraints into random order semi-streaming algorithms. The other tool is a semi-streaming variant of a recently proposed offline algorithm for matroid constraints.