Cuckoo Hashing

Abstract

We present a simple and efficient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (<em>Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738-761, 1994</em>). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of the scheme is backed by extensive experiments and comparisons with known methods, showing it to be quite competitive also in the average case.

Some Open Questions Related to Cuckoo Hashing

“…Hence, in general, we refer to the entire range of variations as cuckoo hashing, and clarify in context when necessary. For cuckoo hashing the case of d = 2 choices with one item per bucket is now well understood [32,27], the cases with more choices and more items per bucket have left many remaining open questions [15,17]. The case of d = 2 is so well understood because there is a direct correspondence to random graphs.…”

“…Cuckoo hashing [32] is a further variation on multiple choice hashing schemes. In the original description, an item can be placed in one of two possible buckets.…”

Oblivious RAM Revisited

“…) 9. If the Cuckoo hashing fails (due to cycles, see [17]), choose new random secret hash functions h i+1, +1 0,k and h i+1, +1…”

“…Cuckoo hashing [16,17] is a relatively new hashing algorithm, which in its basic form maps each item to one of two potential entries of a hash table, while ensuring constant lookup and deletion time in the worst case, and amortized constant time for insertions.…”

“…In comparison, our construction uses Cuckoo hashing [16,17], which is a hashing scheme mapping n items to 2(1 + )n bins with the guarantee that at most a single item is mapped into a bin. Consequently, the construction uses a total of only O(n) server storage.…”