Submodular Maximization over Sliding Windows

TL;DR

This paper introduces algorithms for submodular maximization over sliding windows in data streams, extending existing streaming methods to recent data with applications to real-world datasets.

Contribution

It provides a reduction from sliding window to standard streaming models, enabling new algorithms for monotone and non-monotone submodular maximization under various constraints.

Findings

First algorithms for sliding window submodular maximization under cardinality and matroid constraints

Effective heuristics demonstrated on real-world datasets

General reduction applicable to various constraints

Abstract

In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent data, and study the maximization problem over sliding windows. We provide a general reduction from the sliding window model to the standard streaming model, and thus our approach works for general constraints as long as there is a corresponding streaming algorithm in the standard streaming model. As a consequence, we obtain the first algorithms in the sliding window model for maximizing a monotone/non-monotone submodular function under cardinality and matroid constraints. We also propose several heuristics and show their efficiency in real-world datasets.