On the dynamization of data structures

In this paper we present a simple dynamization method that preserves the query and storage costs of a static data structure and ensures reasonable update costs. In this method, the majority of data elements are maintained in a single data structure, and the updates are handled using "smaller" auxiliary data structures. We analyze the query, storage, and amortized update costs for the dynamic version of a static data structure in terms of a function f, such that f(n)<n, that bounds the sizes of the auxiliary data structures (where n is the number of elements in the data structure). The conditions on f for minimal (with respect to asymptotic upper bounds) amortized update costs are then obtained. The proposed method is shown to be particularly suited for the cases where the merging of two data structures is more efficient than building the resultant data structure from scratch. Its effectiveness is illustrated by applying it to a class of data structures that have linear merging cost; this class consists of data structures such as Voronoi diagrams, K-d trees, quadtrees, multiple attribute trees, etc.