Distributed Computing

In this paper we study the MapReduce Class (MRC) defined by Karloff et al., which is a formal complexity-theoretic model of MapReduce. 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.

[1]  Rachid Guerraoui,et al.  On obstruction-free transactions , 2008, SPAA '08.

[2]  Robert Ennals.  Software Transactional Memory Should Not Be Obstruction-Free , 2005 .

[3]  Petr Kuznetsov,et al.  On the Cost of Concurrency in Transactional Memory , 2011, OPODIS.

[4]  Hagit Attiya,et al.  The Cost of Privatization in Software Transactional Memory , 2013, IEEE Transactions on Computers.

[5]  Nir Shavit,et al.  TLRW: return of the read-write lock , 2010, SPAA '10.

[6]  Rachid Guerraoui,et al.  Principles of Transactional Memory , 2010, Synthesis Lectures on Distributed Computing Theory.

[7]  Nir Shavit,et al.  Transactional Locking II , 2006, DISC.

[8]  Paul E. McKenney,et al.  Memory Barriers: a Hardware View for Software Hackers , 2010 .

[9]  Maurice Herlihy,et al.  Obstruction-free synchronization: double-ended queues as an example , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[10]  Maurice Herlihy,et al.  Software transactional memory for dynamic-sized data structures , 2003, PODC '03.

[11]  Maurice Herlihy,et al.  Wait-free synchronization , 1991, TOPL.

[12]  D. Rosenkrantz,et al.  Developing self - stabilizing coloring algorithms via systematic randomization , 1994 .

[13]  Petr Kuznetsov,et al.  Why Transactional Memory Should Not Be Obstruction-Free , 2015, ArXiv.

[14]  Roger Wattenhofer,et al.  Symmetry breaking depending on the chromatic number or the neighborhood growth , 2013, Theor. Comput. Sci..

[15]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[16]  Petr Kuznetsov,et al.  Progressive Transactional Memory in Time and Space , 2015, PaCT.

[17]  Rachid Guerraoui,et al.  The semantics of progress in lock-based transactional memory , 2009, POPL '09.

[18]  Idit Keidar,et al.  On maintaining multiple versions in STM , 2010, PODC.

[19]  Virendra J. Marathe,et al.  Adaptive Software Transactional Memory , 2005, DISC.

[20]  Noam Nisan,et al.  Extracting Randomness: A Survey and New Constructions , 1999, J. Comput. Syst. Sci..

[21]  Rachid Guerraoui,et al.  Laws of order: expensive synchronization in concurrent algorithms cannot be eliminated , 2011, POPL '11.

[22]  Nir Shavit,et al.  On the Inherent Sequentiality of Concurrent Objects , 2012, SIAM J. Comput..

[23]  Michael F. Spear,et al.  NOrec: streamlining STM by abolishing ownership records , 2010, PPoPP '10.

[24]  Nir Shavit,et al.  What Really Makes Transactions Faster , 2006 .

[25]  Nathan Linial,et al.  Locality in Distributed Graph Algorithms , 1992, SIAM J. Comput..

[26]  Avi Wigderson,et al.  Pairwise Independence and Derandomization , 2006, Found. Trends Theor. Comput. Sci..

[27]  Lei Xu,et al.  Feedback from nature: an optimal distributed algorithm for maximal independent set selection , 2013, PODC '13.

[28]  Roger Wattenhofer,et al.  A log-star distributed maximal independent set algorithm for growth-bounded graphs , 2008, PODC '08.

[29]  Rachid Guerraoui,et al.  The complexity of obstruction-free implementations , 2009, JACM.

[30]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[31]  Christel Baier,et al.  Probabilistic ω-automata , 2012, JACM.

[32]  Maurice Herlihy,et al.  On the Nature of Progress , 2011, OPODIS.

[33]  Hagit Attiya,et al.  Inherent limitations on disjoint-access parallel implementations of transactional memory , 2009, SPAA '09.

[34]  Keir Fraser,et al.  Practical lock-freedom , 2003 .

[35]  Moni Naor,et al.  What can be computed locally? , 1993, STOC.