Improved Sliding Window Algorithms for Clustering and Coverage via Bucketing-Based Sketches

Abstract

Streaming computation plays an important role in large-scale data analysis. The sliding window model is a model of streaming computation which also captures the recency of the data. In this model, data arrives one item at a time, but only the latest $W$ data items are considered for a particular problem. The goal is to output a good solution at the end of the stream by maintaining a small summary during the stream. In this work, we propose a new algorithmic framework for designing efficient sliding window algorithms via bucketing-based sketches. Based on this new framework, we develop space-efficient sliding window algorithms for $k$-cover, $k$-clustering and diversity maximization problems. For each of the above problems, our algorithm achieves $(1\pm \varepsilon)$-approximation. Compared with the previous work, it improves both the approximation ratio and the space.