Dynamic k-dimensional multiway search under time-varying access frequencies

Abstract

We consider multiway search trees for k-dimensional search under time-varying access frequencies. Let S = {k_l,...,k_n} be a set of k-dimensional keys, k≥1, and let p ^t_i be the number of accesses to k_i, also called frequency of k_i, up to time t, $W^t = \sum\limits_{i = 1}^n {p_i^t }$. We present weighted (k+1)B-trees of order d, d≥1, with the following properties:

• 1. A search for key k_i can be performed in time 0(min(n,log_d+1W^t/p ^t_i )+(k−1)), i.e. the tree is always nearly optimal.

• 2. The time for updating after a search is at most proportional to search time.

• 3. Insertion of a new key with arbitrary frequency as well as deletion of a key with arbitrary frequency can be carried out in time 0(min(n,log_d+1W^t)+(k−1)).