Simpler insertion algorithms for high-load d-ary cuckoo hashing

Determine whether simpler insertion algorithms, such as random-walk or breadth-first-search insertion, achieve polynomial-in-\(\epsilon^{-1}\) time bounds when the number of hash functions is \(d=\Theta(\ln \epsilon^{-1})\).

Background

The paper establishes efficient insertion for bubble-up cuckoo hashing with d=⌈ln⁡ϵ−1+α⌉d=\lceil\ln \epsilon^{-1}+\alpha\rceil hash locations, but it does not resolve whether substantially simpler policies already achieve polynomial expected insertion time at the same asymptotic number of hash functions. The authors note that this outcome is widely believed but technically difficult to prove.

References

Several major open questions remain. Do simpler algorithms (e.g., random-walk or BFS) already get good time bounds (e.g., $poly \epsilon{-1}$) when $d = \Theta(\ln \epsilon{-1})$? It is widely believed that the answer should be yes, but proving this remains difficult.

— Efficient $d$-ary Cuckoo Hashing at High Load Factors by Bubbling Up  (2501.02312 - Kuszmaul et al., 4 Jan 2025) in Section Conclusion