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Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing

Authors Xinyu Mao , Guangxu Yang , Jiapeng Zhang

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  • Theory of computation → Communication complexity
Keywords
  • communication complexity
  • lifting theorems
  • pointer chasing

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Abstract

We prove an Ω(n / k + k) communication lower bound on (k - 1)-round distributional complexity of the k-step pointer chasing problem under uniform input distribution, improving the Ω(n/k - klog n) lower bound due to Yehudayoff (Combinatorics Probability and Computing, 2020). Our lower bound almost matches the upper bound of Õ(n/k + k) communication by Nisan and Wigderson (STOC 91). 
As part of our approach, we put forth gadgetless lifting, a new framework that lifts lower bounds for a family of restricted protocols into lower bounds for general protocols. A key step in gadgetless lifting is choosing the appropriate definition of restricted protocols. In this paper, our definition of restricted protocols is inspired by the structure-vs-pseudorandomness decomposition by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24).
Previously, round-communication trade-offs were mainly obtained by round elimination and information complexity. Both methods have some barriers in some situations, and we believe gadgetless lifting could potentially address these barriers.

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Xinyu Mao, Guangxu Yang, and Jiapeng Zhang. Gadgetless Lifting Beats Round Elimination: Improved Lower Bounds for Pointer Chasing. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.75

Author Details

Xinyu Mao
  • Thomas Lord Department of Computer Science, University of Southern California, Los Angeles, CA, USA
Guangxu Yang
  • Thomas Lord Department of Computer Science, University of Southern California, Los Angeles, CA, USA
Jiapeng Zhang
  • Thomas Lord Department of Computer Science, University of Southern California, Los Angeles, CA, USA

Funding

  • Mao, Xinyu: Supported by NSF CAREER award 2141536.
  • Yang, Guangxu: Supported by NSF CAREER award 2141536.
  • Zhang, Jiapeng: Supported by NSF CAREER award 2141536.

Acknowledgements

We thank Sepehr Assadi, Yuval Filmus and anonymous reviewers for their helpful comments.

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