Formal analysis of PtrHash’s hash-evict pilot-placement

Establish a rigorous probabilistic analysis that proves the hash-evict pilot-search procedure used by PtrHash—where buckets are inserted from large to small, and when no collision-free 8-bit pilot exists a pilot minimizing weighted collisions is chosen and colliding buckets are evicted—succeeds with high probability under clearly specified conditions on parameters such as the number of slots per part, the average bucket size λ, the load factor α, and the chosen bucket assignment function γ.

Background

PtrHash constructs a minimal perfect hash function using fixed-width 8-bit pilots and a cuckoo-hashing-like eviction strategy (“hash-evict”) when a collision-free pilot cannot be found for a bucket. While experiments indicate the approach works well in practice, the paper notes the absence of a formal theoretical guarantee of success.

The authors suggest that extending existing analyses (e.g., those developed for related methods such as PHOBIC) could yield a proof that, under appropriate parameter settings, the hash-evict strategy succeeds with high probability.