Polynomial-time insertion with logarithmic bucket size

Establish whether bucketized cuckoo hashing with bucket size \(b=\Theta(\log \epsilon^{-1})\) can support insertions taking polynomial time in \(\epsilon^{-1}\).

Background

For bucketized cuckoo hashing, the paper asks whether logarithmic bucket size suffices for polynomial-in-ϵ−1\epsilon^{-1} insertion time. This is presented as one of the major unresolved goals in the bucketized setting, whose analysis is complicated by spoiled randomness.

References

Within the study of bucketized cuckoo hashing, there are several goals that would be interesting to accomplish. (See, also, the discussion of bucketized cuckoo hashing in the related-work portion of the introduction.) Major questions include: Can one achieve $poly \epsilon{-1}$-time insertions with buckets of size $b = \Theta(\log \epsilon{-1})$?

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