Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

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 thei...

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Bibliographic Details
Published in:Algorithmica Vol. 81; no. 6; pp. 2222 - 2243
Main Authors: Huang, Zengfeng, Yi, Ke, Zhang, Qin
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2019
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Communication
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Finishes
Lower bounds
Mathematics of Computing
Randomization
Theory of Computation
Tracking problem
Continuous distributed tracking
Distributed streaming
Randomized algorithms
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-018-00531-y