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.
翻译:我们证明,用于相关性聚类的Pivot算法的一种简单单遍半流变体,使用O(n/{\epsilon})字内存即可实现(3 + {\epsilon})近似比。这一结果略优于近期Cambus、Kuhn、Lindy、Pai和Uitto的工作(使用O(n log n)字内存实现(3 + {\epsilon})近似比),以及Behnezhad、Charikar、Ma和Tan的工作(使用O(n)字内存实现5近似比)。本文的主要贡献之一在于,该算法及其分析均极为简洁,且算法易于实现。