Asymmetric Hashing in Data Structure

In this section we will see what is Asymmetric Hashing technique. In this technique, the hash table is split into d number of blocks. Each split is of length n/d. The probe value xi, 0 ≤ i ≤ d, is drawn uniformly from $$\lbrace\frac{i*n}{d},...,\frac{(i+1)*n}{d-1}\rbrace$$. As with multiple choice hashing, to insert x, the algorithm checks the length of the list A[x₀], A[x₁], . . ., A[x_{d – 1}]. Then appends x to the shortest of these lists. If there is a tie, then it inserts x to the list with smallest index.

According to Vocking, the expected length of longest list for asymmetric hashing is −

$$E[W]\leq\frac{ln\:ln\:n}{d\:ln\:\phi_{2}}+O(1)$$

The function 𝜙_𝑑 is a generalization of golden ratio, so $$\phi_{2}=\frac{(1+\sqrt{5})}{2}$$