Low rank approximation and regression in input sparsity time
Kenneth L. Clarkson, David P. Woodruff
STOC 2013
We consider a number of fundamental statistical and graph problems in the message-passing model, where we have k machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the k data sets. The communication is point-to-point, and the goal is to minimize the total communication among the k machines. This model captures all point-to-point distributed computational models with respect to minimizing communication costs. Our analysis shows that exact computation of many statistical and graph problems in this distributed setting requires a prohibitively large amount of communication, and often one cannot improve upon the communication of the simple protocol in which all machines send their data to a centralized server. Thus, in order to obtain protocols that are communication-efficient, one has to allow approximation, or investigate the distribution or layout of the data sets.
Kenneth L. Clarkson, David P. Woodruff
STOC 2013
Haim Avron, Vikas Sindhwani, et al.
NeurIPS 2013
Alexandr Andoni, Jiecao Chen, et al.
ITCS 2016
Kenneth L. Clarkson, David P. Woodruff
Journal of the ACM