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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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ACM Subject Classification
  • 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.

Cite As Get BibTex

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.

References

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