Author

A. Conway

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Preprint Aug 2026

Tight Bounds for Memory Allocation With and Without Request Fragmentation

The classical memory-allocation problem captures the task of placing objects of different sizes in memory, while minimizing the so-called memory high-water mark. It has been known since the early 1970s that the optimal competitive ratio for any deterministic online allocator is $\Theta(\log M)$, where $M$ is the volume...

Michael A. Bender, A. Conway, Martín Farach-Colton et al. · 1 citation

Preprint Aug 2026

Lower Bounds for Linear Hashing via Arithmetic Kakeya

Affine modular linear hashing is one of the simplest classical hash families. For a prime $p>u$, the hash function is obtained by choosing $s,t$ uniformly from $\mathbb{Z}_p$ and mapping each key $x \in \{0,\ldots,u-1\}$ to one of $n$ bins by $h(x) = [(sx+t) \bmod p] \bmod n$. Despite its simplicity, the maximum load o...

Ainesh Bakshi, A. Conway, Hanna Komlós et al. · 1 citation