Abstract
We begin with a brief survey of the literature concerning the Interpolation Search algorithm, then provide a detailed description of the algorithm and how to implement it to search a particular table or file. We next analyze the complexity of the search method by investigating the moments of the distribution of the number of table accesses needed to locate a given record. For a table containing n entries, we find that the expected value of the number of accesses is log2 log2 n+O(1) and that the variance is O(log2 log2 n). Lastly we provide some approximations for the expected value for the successful and unsuccessful search in such a table.
Similar content being viewed by others
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. New York: Dover 1964
De Bruijn, N.G.: Asymptotics Methods in Analysis. Amsterdam: North Holland 1970
Gonnet, G.H.: Unpublished notes on Average Number of Accesses to Files. Universidad de la Republica, Montevideo, Uruguay, Aug. 1972
Gonnet, G.H.: Interpolation and Interpolation-Hash Searching, PhD Thesis. Waterloo: University of Waterloo 1977
Gonnet, G.H.: Notes on the Derivation of Asymptotic Expansions from Summations. Information Processing Letters 7, 165–169 (1978)
Gonnet, G.H., Rogers, L.D.: The Interpolation-Sequential Search Algorithm. Information Processing Letters 6, 136–139 (1977)
Knuth, D.E.: The Art of Computer Programming. Vol. 3, Sorting and Searching. Ontario: Addison-Wesley Don Mills 1973
Knuth, D.E.: Final Exam. & Solutions of Final Exam. Course Cs 255. Stanford University 1976
Kruijer, H.S.M.: The Interpolated File Search Method. Informatie 16, 612–615 (1974)
Peterson, W.W.: Addressing for Random-Access Storage. IBM Journal of Research and Development 1, 130–146 (1957)
Perl, Y., Itai, A., Avni, H.: Interpolation Search — A Log Log N Search. Comm. A.C.M. 21, 550–557 (1978)
Perl, Y., Reingold, E.M.: Understanding the Complexity of Interpolation Search. Information Processing Letters 6, 219–221 (1977)
Price, C.E.: Table Lookup Techniques. Computing Surveys 3, 56–58 (1971)
Yao, A.C., Yao, F.F.: The Complexity of Searching an Ordered Random Table. Proceedings of the Symposium on Fundations of Computer Science, Houston 1976, pp. 173–176
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gonnet, G.H., Rogers, L.D. & Alan George, J. An algorithmic and complexity analysis of interpolation search. Acta Informatica 13, 39–52 (1980). https://doi.org/10.1007/BF00288534
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00288534