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arXiv · 2403.03990

A Sierpinski Triangle Data Structure for Efficient Array Value Update and Prefix Sum Calculation

Brent Harrison·Jason Necaise·Andrew Projansky·James D. Whitfield
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Abstract

The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data structure resembling the Sierpinski triangle, which accomplishes these operations with the same memory usage in $O(\log_3 N)$ time instead. We show this order to be optimal by making use of a connection to quantum computing.

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Brent Harrison, Jason Necaise, Andrew Projansky, James D. Whitfield. 2024-03-06. A Sierpinski Triangle Data Structure for Efficient Array Value Update and Prefix Sum Calculation. https://arxiv.org/abs/2403.03990

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