[2606.30948] The Fourth-Root Complexity of Data Movement

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arXiv:2606.30948 (cs)

[Submitted on 29 Jun 2026]

Title:The Fourth-Root Complexity of Data Movement

Authors:Chen Ding<br>View a PDF of the paper titled The Fourth-Root Complexity of Data Movement, by Chen Ding

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Abstract:Time complexity typically assumes $O(1)$ cost per data access. This paper presents an analysis based on an abstract memory hierarchy. For a common class of applications, it shows that the data-access cost scales with the fourth root of data size, that is, as data size $N$ increases, the cost of each access increases at the rate of $N^\frac{1}{4}$.

While the analysis does not predict performance, it predicts scalability. Specifically, the paper provides a precise analysis that shows the constant-factor difference between cases where the miss ratio follows a power law versus an exponential decay.

Subjects:

Computational Complexity (cs.CC); Performance (cs.PF); Programming Languages (cs.PL)

Cite as:<br>arXiv:2606.30948 [cs.CC]

(or<br>arXiv:2606.30948v1 [cs.CC] for this version)

https://doi.org/10.48550/arXiv.2606.30948

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Chen Ding [view email]<br>[v1]<br>Mon, 29 Jun 2026 22:01:50 UTC (228 KB)

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