On Streaming and Communication Complexity of the Set Cover Problem
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Demaine_On streaming.pdf
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Author(s)
Demaine, Erik D.
Indyk, Piotr
Mahabadi, Sepideh
Vakilian, Ali
Date Issued
2014
Journal
Distributed Computing
Publisher
Springer-Verlag
Citation
Demaine, Erik D., Piotr Indyk, Sepideh Mahabadi, and Ali Vakilian. “On Streaming and Communication Complexity of the Set Cover Problem.” Distributed Computing (2014): 484–498.
Version
Author's final manuscript
Abstract
We develop the first streaming algorithm and the first two-party communication protocol that uses a constant number of passes/rounds and sublinear space/communication for logarithmic approximation to the classic Set Cover problem. Specifically, for n elements and m sets, our algorithm/protocol achieves a space bound of O(m ·n [superscript δ] log[superscript 2] n logm) using O(4[superscript 1/δ]) passes/rounds while achieving an approximation factor of O(4[superscript 1/δ]logn) in polynomial time (for δ = Ω(1/logn)). If we allow the algorithm/protocol to spend exponential time per pass/round, we achieve an approximation factor of O(4[superscript 1/δ]). Our approach uses randomization, which we show is necessary: no deterministic constant approximation is possible (even given exponential time) using o(m n) space. These results are some of the first on streaming algorithms and efficient two-party communication protocols for approximation algorithms. Moreover, we show that our algorithm can be applied to multi-party communication model.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-662-45174-8_33
