The Fourth-Root Complexity of Data Movement

Chen Ding

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arXiv · 2606.30948

The Fourth-Root Complexity of Data Movement

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.

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BibTeX RIS

Chen Ding. 2026-06-29. The Fourth-Root Complexity of Data Movement. https://arxiv.org/abs/2606.30948

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