Space Efficient Hash Tables with Worst Case Constant Access Time

We generalize Cuckoo Hashing \cite{PagRod01} to \emph{$d$-ary Cuckoo Hashing} and show how this yields a simple hash table data structure that stores $n$ elements in $(1+\epsilon)\,n$ memory cells, for any constant $\epsilon > 0$. Assuming uniform hashing, accessing or deleting table entries takes at most $d = O(\ln\frac{1}{\epsilon})$ 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 $(1+\epsilon)\,n$ space, and supports satellite information. Experiments indicate that $d=4$ choices suffice for $\epsilon \approx 0.03$. We also describe a hash table data structure using explicit constant time hash functions, using at most $d= O(\ln^2\frac{1}{\epsilon})$ probes in the worst case. A corollary is an expected linear time algorithm for finding maximum cardinality matchings in a rather natural model of sparse random bipartite graphs