Analyze random-walk insertion for bucketized cuckoo hashing

Determine whether random-walk insertions in bucketized cuckoo hashing achieve efficient insertion bounds comparable to those known for breadth-first-search insertion.

Background

Bucketized cuckoo hashing assigns each element to two buckets of size b. Existing work cited in the paper establishes bounds for breadth-first-search insertion, while efficient random-walk insertion remains unresolved, in part because repeated evictions expose the algorithm to previously revealed or “spoiled” randomness.

References

They left as an open question whether one could prove a similar result for random-walk insertions.

— Efficient $d$-ary Cuckoo Hashing at High Load Factors by Bubbling Up  (2501.02312 - Kuszmaul et al., 4 Jan 2025) in Related Work, paragraph beginning “An alternative to $d$-ary cuckoo hashing is bucketized cuckoo hashing”