Analyze simpler insertion policies at logarithmic hash degree

Determine whether simpler insertion algorithms, such as random-walk or breadth-first-search insertion, achieve polynomial-in-epsilon^{-1} time bounds for d-ary cuckoo hashing when d=Theta(ln epsilon^{-1}).

Background

The paper establishes efficient insertion bounds for the specialized bubble-up cuckoo hashing algorithm with d close to ln epsilon{-1}. It leaves unresolved whether more standard insertion policies, particularly random-walk and breadth-first-search policies, can obtain polynomial insertion time under the same asymptotic hash-degree regime.

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 Conclusion