On the Computational Complexity of MapReduce

Abstract : In this paper we study the MapReduce Class (MRC) defined by Karloff et al., which is a formal complexity-theoretic model of MapRe-duce. We show that constant-round MRC computations can decide regular languages and simulate sublogarithmic space-bounded Turing machines. In addition, we prove hierarchy theorems for MRC under certain complexity-theoretic assumptions. These theorems show that sufficiently increasing the number of rounds or the amount of time per processor strictly increases the computational power of MRC. Our work lays the foundation for further analysis relating MapReduce to established complexity classes. Our results also hold for Valiant's BSP model of parallel computation and the MPC model of Beame et al.
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Yoram Moses; Matthieu Roy. DISC 2015, Oct 2015, Tokyo, Japan. Springer-Verlag Berlin Heidelberg, LNCS 9363, 29th International Symposium on Distributed Computing. 〈10.1007/978-3-662-48653-5_1〉
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Benjamin Fish, Jeremy Kun, Ádám D. Lelkes, Lev Reyzin, György Turán. On the Computational Complexity of MapReduce. Yoram Moses; Matthieu Roy. DISC 2015, Oct 2015, Tokyo, Japan. Springer-Verlag Berlin Heidelberg, LNCS 9363, 29th International Symposium on Distributed Computing. 〈10.1007/978-3-662-48653-5_1〉. 〈hal-01199793〉

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