Dynamic k-Dimensional Multiway Search under Time-Varying Access Frequencies

We consider multiway search trees for k-dimensional search under time-varying access frequencies. Let S = {kl,...,kn} be a set of k-dimensional keys, k≥1, and let p i t be the number of accesses to ki, also called frequency of ki, 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 ki can be performed in time 0(min(n,logd+1Wt/p i t )+(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,logd+1Wt)+(k−1)).