Single-Pass Pivot Algorithm for Correlation Clustering. Keep it simple!

TL;DR

This paper introduces a simple, efficient single-pass semi-streaming algorithm for correlation clustering that achieves a near-optimal approximation with less memory than previous methods, and is easy to implement.

Contribution

It presents a straightforward single-pass semi-streaming algorithm for correlation clustering with improved memory efficiency and simplicity over prior approaches.

Findings

Achieves a (3 + ε)-approximation with O(n/ε) memory

Improves over previous algorithms with higher memory usage

The algorithm is simple and easy to implement

Abstract

We show that a simple single-pass semi-streaming variant of the Pivot algorithm for Correlation Clustering gives a (3 + {\epsilon})-approximation using O(n/{\epsilon}) words of memory. This is a slight improvement over the recent results of Cambus, Kuhn, Lindy, Pai, and Uitto, who gave a (3 + {\epsilon})-approximation using O(n log n) words of memory, and Behnezhad, Charikar, Ma, and Tan, who gave a 5-approximation using O(n) words of memory. One of the main contributions of this paper is that both the algorithm and its analysis are very simple, and also the algorithm is easy to implement.