The Communication Complexity of Distributed ε-Approximations

Data summarization is an effective approach to dealing with the “big data” problem. Whiledata summarization problems traditionally have been studied is the streaming model, the focus isstarting to shift to distributed models, as distributed/parallel computation seems to be the only viableway to handle today’s massive data sets. In this paper, we study ε-approximations, a classical datasummary that, intuitively speaking, preserves approximately the density of the underlying data setover a certain range space. We consider the problem of computing ε-approximations for a data setwhich is held jointly by k players, and give general communication upper and lower bounds thathold for any range space whose discrepancy is known. ∗Zengfeng Huang is supported by the Danish National Research Foundation grant DNRF84 through Center for MassiveData Algorithmics (MADALGO).†Ke Yi is supported by HKRGC under grants GRF-621413 and GRF-16211614.