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Brief Announcement: On Polynomial-Time Local Decision

Published: 21 July 2022 Publication History

Abstract

In distributed graph algorithms, a key computational resource is the communication radius of the algorithm, i.e., its locality. The class LD captures the distributed languages that can be decided by a local algorithm; its nondeterministic analog is the class NLD, which captures the distributed languages that can be decided by a local algorithm with local advice. Inspired by the polynomial hierarchy in complexity theory, this has been further extended into a hierarchy of local decision, where each node runs an alternating Turing machine. However, in prior work, the computational efficiency of each network node as nodes where allowed to run Turing machines for unbounded number of steps. This results in some undesirable and unanticipated properties: for example, the class NLD includes some Turing-undecidable languages.

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MP4 File (S1-T5-BA.mp4)
Brief-announcement presentation video

References

[1]
Alkida Balliu, Gianlorenzo D'Angelo, Pierre Fraigniaud, and Dennis Olivetti. 2018. What can be verified locally? J. Comput. System Sci. 97 (2018), 106--120.
[2]
Laurent Feuilloley, Pierre Fraigniaud, and Juho Hirvonen. 2021. A hierarchy of local decision. Theoretical Computer Science 856 (2021), 51--67.
[3]
Pierre Fraigniaud, Mika Göös, Amos Korman, and Jukka Suomela. 2013. What can be decided locally without identifiers?. In Proceedings of the 2013 ACM symposium on Principles of distributed computing. ACM, New York, NY, USA, 157--165.
[4]
Pierre Fraigniaud, Magnús M Halldórsson, and Amos Korman. 2012. On the impact of identifiers on local decision. In International Conference On Principles Of Distributed Systems. Springer, Berlin, Heidelberg, 224--238.
[5]
Pierre Fraigniaud, Amos Korman, and David Peleg. 2013. Towards a complexity theory for local distributed computing. Journal of the ACM (JACM) 60, 5 (2013), 1--26.
[6]
William I Gasarch. 2019. Guest column: The third P=? NP poll. ACM SIGACT News 50, 1 (2019), 38--59.
[7]
Juris Hartmanis and Richard E Stearns. 1965. On the computational complexity of algorithms. Trans. Amer. Math. Soc. 117 (1965), 285--306.

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cover image ACM Conferences
PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
July 2022
509 pages
ISBN:9781450392624
DOI:10.1145/3519270
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Publication History

Published: 21 July 2022

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Author Tags

  1. local decision
  2. nondeterministic decision
  3. polynomial hierarchy

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