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Brief Announcement: Relations Between Space-Bounded and Adaptive Massively Parallel Computations

Authors Michael Chen, A. Pavan, N. V. Vinodchandran



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Author Details

Michael Chen
  • Iowa State University, Ames, IA, USA
A. Pavan
  • Iowa State University, Ames, IA, USA
N. V. Vinodchandran
  • University of Nebraska–Lincoln, NE, USA

Acknowledgements

The authors thank Sriram Pemmaraju and Meena Mahajan for their helpful discussions. We thank anonymous reviewers for their valuable comments and pointers to some critical references.

Cite AsGet BibTex

Michael Chen, A. Pavan, and N. V. Vinodchandran. Brief Announcement: Relations Between Space-Bounded and Adaptive Massively Parallel Computations. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 37:1-37:7, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DISC.2023.37

Abstract

In this work, we study the class of problems solvable by (deterministic) Adaptive Massively Parallel Computations in constant rounds from a computational complexity theory perspective. A language L is in the class AMPC⁰ if, for every ε > 0, there is a deterministic AMPC algorithm running in constant rounds with a polynomial number of processors, where the local memory of each machine s = O(N^ε). We prove that the space-bounded complexity class ReachUL is a proper subclass of AMPC⁰. The complexity class ReachUL lies between the well-known space-bounded complexity classes Deterministic Logspace (DLOG) and Nondeterministic Logspace (NLOG). In contrast, we establish that it is unlikely that PSPACE admits AMPC algorithms, even with polynomially many rounds. We also establish that showing PSPACE is a subclass of nonuniform-AMPC with polynomially many rounds leads to a significant separation result in complexity theory, namely PSPACE is a proper subclass of EXP^{Σ₂^{𝖯}}.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Massively parallel algorithms
  • Theory of computation → Complexity classes
Keywords
  • Massively Parallel Computation
  • AMPC
  • Complexity Classes
  • LogSpace
  • NL
  • PSPACE

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References

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