In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without reordering elements over time, it is possible to construct a hash table that achieves far better expected search complexities (both amortized and worst-case) than were previously thought possible. Along the way, we disprove the central conjecture left by Yao in his seminal paper 'Uniform Hashing is Optimal'. All of our results come with matching lower bounds.
Huacheng Yu's team later proved that the Bender et al.'s hash table was as efficient as any data structure could possibly be, marking the end of decades-long efforts to solve Peterson's problem regarding the optimal balance between time and space efficiency in hash tables.
