This interview introduces the results of two papers, one published at SODA 2014, one at DISC 2013.
——– SODA 2014 ————
Title: An Optimal Lower Bound for Distinct Elements in the Message Passing Model
Abstract: In the message-passing model of communication, there are k players each with their own private input, who try to compute or approximate a function of their inputs by sending messages to one another over private channels. We consider the setting in which each player holds a subset S_i of elements of a universe of size n, and their goal is to output a (1+\eps)-approximation to the total number of distinct elements in the union of the sets S_i with constant probability, which can be amplified by independent repetition. This problem has applications in data mining, sensor networks, and network monitoring. We resolve the communication complexity of this problem up to a constant factor, for all settings of n, k and \eps, by showing a lower bound of \Omega(k \cdot \min(n, 1/\eps^2) + k \log n) bits. This improves upon previous results, which either had non-trivial restrictions on the relationships between the values of n, k and \eps, or were suboptimal by logarithmic factors, or both.
———- DISC 2013 —————–
Title: When Distributed Computation is Communication Expensive