Abstract
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 functionf, such thatf(n)<n, that bounds the sizes of the auxiliary data structures (wheren is the number of elements in the data structure). The conditions onf 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. L. Bentley and J. B. Saxe,Decomposable searching problems I:Static-to-dynamic transformations, J. of Algorithms 1, 1980, pp. 571–577.
I. G. Gowda and D. G. Kirkpatrick,Exploiting linear merging and extra storage in the maintenance of fully dynamic geometric data structures, Proc. 19th Annual Allerton Conf. on Communication, Control and Computing, 1980, pp. 1–10.
D. T. Lee and F. P. Preparata,Computational geometry — a survey, IEEE Trans. Computers C-33 (12), Dec. 1985, pp. 1072–1101.
K. Mehlhorn,Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry, Springer-Verlag, 1984.
S. V. N. Rao, S. S. Iyengar and C. E. V. Madhavan,A comparative study of multiple attribute tree and inverted file structures for large bibliographic files, Information Process. and Mgmt. 21, (5), 1985, pp. 433–442.
M. H. Overmars,The Design of Dynamic Data Structures, Lecture Notes in Computer Science No. 156, Springer-Verlag, 1984.
F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rao, N.S.V., Vaishnavi, V.K. & Sitharama Iyengar, S. On the dynamization of data structures. BIT 28, 37–53 (1988). https://doi.org/10.1007/BF01934693
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934693