Submodular Streaming in All its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity

TL;DR

This paper introduces Sieve-Streaming++, a streaming algorithm for monotone submodular maximization that achieves tight approximation with minimal memory and adaptive complexity, and extends it to multi-source streaming.

Contribution

The paper presents a new streaming algorithm with tight approximation guarantees, reduced memory usage, and lower adaptive complexity, including extensions to multi-source streaming scenarios.

Findings

Achieves a tight (1/2)-approximation with O(k) memory.

Reduces adaptive rounds and computational complexity.

Demonstrates efficiency on real-world data streams.

Abstract

Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a cardinality constraint $k$. We first propose Sieve-Streaming++, which requires just one pass over the data, keeps only $O(k)$ elements and achieves the tight $(1/2)$-approximation guarantee. The best previously known streaming algorithms either achieve a suboptimal $(1/4)$-approximation with $\Theta(k)$ memory or the optimal $(1/2)$-approximation with $O(k\log k)$ memory. Next, we show that by buffering a small fraction of the stream and applying a careful filtering procedure, one can heavily reduce the number of adaptive computational rounds, thus substantially lowering the computational complexity of Sieve-Streaming++. We then generalize our results to the more challenging multi-source streaming setting. We show how one can achieve the tight $(1/2)$-approximation guarantee with $O(k)$ shared memory while minimizing not only the required rounds of computations but also the total number of communicated bits. Finally, we demonstrate the efficiency of our algorithms on real-world data summarization tasks for multi-source streams of tweets and of YouTube videos.