Distributed Partial Clustering

Abstract

Recent years have witnessed an increasing popularity of algorithm design for distributed data, largely due to the fact that massive datasets are often collected and stored in different locations. In the distributed setting, communication typically dominates the query processing time. Thus, it becomes crucial to design communication-efficient algorithms for queries on distributed data. Simultaneously, it has been widely recognized that partial optimizations, where we are allowed to disregard a small part of the data, provide us significantly better solutions. The motivation for disregarded points often arises from noise and other phenomena that are pervasive in large data scenarios. In this article, we focus on partial clustering problems, k -center, k -median, and k -means objectives in the distributed model, and provide algorithms with communication sublinear of the input size. As a consequence, we develop the first algorithms for the partial k -median and means objectives that run in subquadratic running time. We also initiate the study of distributed algorithms for clustering uncertain data, where each data point can possibly fall into multiple locations under certain probability distribution.