Space Efficient Hash Tables with Worst Case Constant Access Time

Dimitris Fotakis, Rasmus Pagh, Peter Sanders, Paul G. Spirakis

Abstract: We generalize Cuckoo Hashing [16] to d-ary Cuckoo Hashing and show how this yields a simple hash table data structure that stores n elements in (1 + ∈) n memory cells, for any constant ∈ > 0. Assuming uniform hashing, accessing or deleting table entries takes at most d = O(ln 1/∈ ) 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+∈) n space, and supports satellite information. Experiments indicate that d = 4 choices suffice for ∈ ≈ 0.03. We also describe a hash table data structure using explicit constant time hash functions, using at most d = O(ln2 1/∈ ) 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.