On Streaming and Communication Complexity of the Set Cover Problem
Author(s)Demaine, Erik D.; Indyk, Piotr; Mahabadi, Sepideh; Vakilian, Ali
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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.
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