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• W2902899861 abstract "The goal of this article is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in motivating application domains, such as graph connectivity problems. We introduce an abstract model of massively parallel computation, where essentially the only restrictions are that the “fan-in” of each machine is limited to s bits, where s is smaller than the input size n , and that computation proceeds in synchronized rounds, with no communication between different machines within a round. Lower bounds on the round complexity of a problem in this model apply to every computing platform that shares the most basic design principles of MapReduce-type systems. We prove that computations in our model that use few rounds can be represented as low-degree polynomials over the reals. This connection allows us to translate a lower bound on the (approximate) polynomial degree of a Boolean function to a lower bound on the round complexity of every (randomized) massively parallel computation of that function. These lower bounds apply even in the “unbounded width” version of our model, where the number of machines can be arbitrarily large. As one example of our general results, computing any nontrivial monotone graph property—such as connectivity—requires a super-constant number of rounds when every machine receives only a subpolynomial (in n ) number of input bits s . Finally, we prove that, in two senses, our lower bounds are the best one could hope for. For the unbounded-width model, we prove a matching upper bound. Restricting to a polynomial number of machines, we show that asymptotically better lower bounds would separate P from NC 1 ." @default.
• W2902899861 created "2018-12-11" @default.
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• W2902899861 date "2018-11-22" @default.
• W2902899861 modified "2023-09-23" @default.
• W2902899861 title "Shuffles and Circuits (On Lower Bounds for Modern Parallel Computation)" @default.
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• W2902899861 doi "https://doi.org/10.1145/3232536" @default.
• W2902899861 hasPublicationYear "2018" @default.
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