Space Efficient Hash Tables With Worst Case Constant Access Time

We generalize Cuckoo Hashing to \emph{$d$-ary Cuckoo Hashing} and show how this yields a simple hash table data structure that stores $n$ elements in $(1+\e)\,n$ memory cells, for any constant $\e > 0$. Assuming uniform hashing, accessing or deleting table entries takes at most $d=\Oh{\ln\frac{1}{\e}}$ probes and the expected amortized insertion time is constant. This is the first dictionary that has worst case constant access time and expected constant update time, works with $(1+\e)\,n$ space, and supports satellite information. Experiments indicate that $d=4$ probes suffice for $\e\approx 0.03$. We also describe variants of the data structure that allow the use of hash functions that can be evaluated in constant time