Single-Pass Streaming Algorithms for Correlation Clustering

Soheil Behnezhad, Moses Charikar, Weiyun Ma, Li-Yang Tan

Abstract: We study correlation clustering in the streaming setting. This problem has been studied extensively and numerous algorithms have been developed, most requiring multiple passes over the stream. For the important case of single-pass algorithms, recent work of Assadi and Wang [8] obtains a c-approximation using Õ(n) space where c > 105 is a constant and n is the number of vertices to be clustered. We present a single-pass algorithm that obtains a 5-approximation using O(n) space. The algorithm itself is extremely simple and has implications beyond the streaming setting (such as for dynamic and local computation algorithms). The approximation analysis, on the other hand, is delicate and in fact tight.