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Computer Science > Computational Complexity

arXiv:2411.10996 (cs)
[Submitted on 17 Nov 2024]

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

Authors:Xinyu Mao, Guangxu Yang, Jiapeng Zhang
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Abstract:We prove an \Omega(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 \Omega(n/k - k log n) lower bound due to Yehudayoff (Combinatorics Probability and Computing, 2020). Our lower bound almost matches the upper bound of O(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.
Subjects: Computational Complexity (cs.CC)
Cite as: arXiv:2411.10996 [cs.CC]
  (or arXiv:2411.10996v1 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.2411.10996

Submission history

From: Xinyu Mao [view email]
[v1] Sun, 17 Nov 2024 08:00:45 UTC (180 KB)
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