Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would like the quality of the clustering in the distributed setting to match that in the centralized setting for which all the data resides on a single site. In this work, we study both graph and geometric clustering problems in two distributed models: (1) a point-to-point model, and (2) a model with a broadcast channel. We give protocols in both models which we show are nearly optimal by proving almost matching communication lower bounds. Our work highlights the surprising power of a broadcast channel for clustering problems; roughly speaking, to spectrally cluster n points or n vertices in a graph distributed across s servers, for a worst-case partitioning the communication complexity in a point-to-point model is n · s, while in the broadcast model it is n + s. A similar phenomenon holds for the geometric setting as well. We implement our algorithms and demonstrate this phenomenon on real life datasets, showing that our algorithms are also very efficient in practice. ∗A preliminary version of this paper appears at the 30th Annual Conference on Neural Information Processing Systems (NIPS), 2016. †Department of Computer Science, Indiana University, Bloomington, USA. Work supported in part by NSF CCF1525024 and IIS-1633215. Email: jiecchen@indiana.edu ‡Department of Computer Science, University of Bristol, Bristol, UK. h.sun@bristol.ac.uk §IBM Research Almaden, San Jose, USA. dpwoodru@us.ibm.com ¶Department of Computer Science, Indiana University, Bloomington, USA. Work supported in part by NSF CCF1525024 and IIS-1633215. Email: qzhangcs@indiana.edu ar X iv :1 70 2. 00 19 6v 1 [ cs .D S] 1 F eb 2 01 7

Communication-Optimal Distributed Clustering∗