Derandomization of Cell Sampling

TL;DR

This paper improves lower bounds on the space complexity of static data structures with non-adaptive query algorithms, refining classical results and providing tighter bounds for specific query complexities.

Contribution

It extends Siegel's classical cell sampling lower bound to non-adaptive data structures, offering improved bounds for all query times t ≥ 2 and specific results for t=2.

Findings

Lower bound s ≥ Ω̃(n·(m/n)^{1/(t-1)}) for non-adaptive data structures

For t=2, lower bound s > m - o(m), surpassing previous bounds

Enhanced understanding of space-query trade-offs in static data structures

Abstract

Since 1989, the best known lower bound on static data structures was Siegel's classical cell sampling lower bound. Siegel showed an explicit problem with $n$ inputs and $m$ possible queries such that every data structure that answers queries by probing $t$ memory cells requires space $s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/t}\right)$. In this work, we improve this bound for non-adaptive data structures to $s\geq\widetilde{\Omega}\left(n\cdot(\frac{m}{n})^{1/(t-1)}\right)$ for all $t \geq 2$. For $t=2$, we give a lower bound of $s>m-o(m)$, improving on the bound $s>m/2$ recently proved by Viola over $\mathbb{F}_2$ and Siegel's bound $s\geq\widetilde{\Omega}(\sqrt{mn})$ over other finite fields.