Author

Jingxun Liang

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Preprint Aug 2026

Optimal Time-Space Tradeoff for Dynamic Difference-Encoded Dictionaries

A dynamic dictionary is constructed that supports operations in $O(\log\varepsilon^{-1}/\log\log\varepsilon^{-1})$ expected amortized time and uses bits of space, and proves a matching lower bound, showing that the time-space tradeoff is optimal even in the \emph{static} case.

G. Blelloch, Yang Hu, William Kuszmaul et al. · 1 citation

Preprint Aug 2026

Quadratic Probing Insertions Are $\epsilon^{-(1+o(1))}$ Time

It is proved that the expected insertion time of the hash table is $\epsilon^{-(1 + o(1))}$.

Yang Hu, William Kuszmaul, Jingxun Liang et al. · 0 citations

Preprint Aug 2026

Quadratic Probing Insertions Are $\epsilon^{-(1+o(1))}$

First proposed in 1968, quadratic probing has stood for more than half a century as one of the simplest and most widely used hash-table designs in computer science. It is conjectured that, at load factor $1 - \epsilon$, the hash table achieves $O(\epsilon^{-1})$ expected insertion time. But even proving a bound of the...

Yang Hu, William Kuszmaul, Jingxun Liang et al. · 0 citations