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Pointer chasing via triangular discrimination

Part of: Communication, information Theory of computing

Published online by Cambridge University Press:  15 May 2020

Amir Yehudayoff
Amir Yehudayoff*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa32000, Israel, Email: amir.yehudayoff@gmail.com
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Abstract

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We prove an essentially sharp $\tilde \Omega (n/k)$ lower bound on the k-round distributional complexity of the k-step pointer chasing problem under the uniform distribution, when Bob speaks first. This is an improvement over Nisan and Wigderson’s $\tilde \Omega (n/{k^2})$ lower bound, and essentially matches the randomized lower bound proved by Klauck. The proof is information-theoretic, and a key part of it is using asymmetric triangular discrimination instead of total variation distance; this idea may be useful elsewhere.

MSC classification

Primary: 68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
Secondary: 94A05: Communication theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 4 , July 2020 , pp. 485 - 494
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

†

Research supported by ISF.

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