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Computing integrated costs of sequences of operations with application to dictionaries

Published: 30 April 1979 Publication History

Abstract

We introduce a notion of integrated cost of a dictionary, as average cost of sequences of search, insert and delete operations. We express generating functions of these sequences in terms of continued fractions; from this we derive an explicit integral expression of integrated costs for three common representations of dictionaries.

References

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Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman, The Design and Analysis of Computer Algorithms (Reading, Mass.: Addison-Wesley, 1974).
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Jon Doyle and Ronald L. Rivest, Linear expected time of a simple Union-Find algorithm, Information Processing Letters 5 (1976), 146-148.
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Philippe Flajolet, Analyse d'Algorithmes de Manipulation de Fichiers, IRIA-Laboria Report N° 321 (August 1978), 28pp.
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Philippe Flajolet, Jean Françon, Gérard Viennot, Jean Vuillemin, "Algorithmique et Combinatoire des Arbres et des Permutations", to appear (1979).
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Jean Françon, Histoires de Fichiers, R.A.I.R.O., Inf. Th. vol 12, pp 49-67, (1978).
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Jean Françon and Gérard Viennot, Permutations selon leur Pics, Creux, Doubles Montées et Doubles Descentes, Nombres d'Euler et de Genocchi. To appear in Discrete Math.
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Arne Jonassen and Ole-Johan Dahl, Analysis of an algorithm for priority queue administration, Math. Inst., University of Olso 1975.
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Gary D. Knott, Deletion in binary storage trees, Ph.D. Thesis, Computer Science Department, Stanford University (May 1975), 93pp.
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Donald E. Knuth, Deletions that preserve randomness IEEE Trans. Soft. Engrg. SE 3 (1977) 351-359.
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Lawrence Snyder, On uniquely represented data structures Proceeding of the 18th Annual Symposium on Foundations of Computer Science, pp. 142-146.
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Robert E. Tarjan, Efficiency of a good but not linear set union algorithm, J.ACM, 22 (1975), 215-225.
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Andrew Chi-Chih Yao, On the average behavior of set merging algorithms, (extended abstract), Proc. ACM Symp. Theory of Computation 8 (1976), 192-195.

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                  cover image ACM Conferences
                  STOC '79: Proceedings of the eleventh annual ACM symposium on Theory of computing
                  April 1979
                  364 pages
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                  Published: 30 April 1979

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                  Author Tags

                  1. Analysis of algorithms
                  2. Continued fractions
                  3. Data structures
                  4. Dictionaries
                  5. Orthogonal polynomials

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                  STOC '79 Paper Acceptance Rate 37 of 111 submissions, 33%;
                  Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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