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 δlog2 n logm) using O(41/δ) passes/rounds while achieving an approximation factor of O(41/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(41/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.
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Demaine, E.D., Indyk, P., Mahabadi, S., Vakilian, A. (2014). On Streaming and Communication Complexity of the Set Cover Problem. In: Kuhn, F. (eds) Distributed Computing. DISC 2014. Lecture Notes in Computer Science, vol 8784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45174-8_33
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DOI: https://doi.org/10.1007/978-3-662-45174-8_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45173-1
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