Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks - Huang, Zengfeng; Yi, Ke; Zhang, Qin (Algorithmica, 2019)
We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the count-tracking problem, where there are k players, each holding a counter n i that gets incremented over time, and the goal is to track an ε -approximation of their sum n = ∑ i n i continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is Θ ( k / ε · log N ) , where N is the final value of n when the tracking finishes, we show that with randomization, the communication cost can be reduced to Θ ( k / ε · log N ) . Our algorithm is simple and uses only O (1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: frequency-tracking and rank-tracking , and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.