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Abstrakty
We give a generic framework to analyze the average-case running time for computing the so called recurrent properties for pairs of binary search trees. Recurrent properties are algorithms that operate on pairs of trees testing some characteristic on nodes by performing a preorder traversal on both trees. Analysis of recurrent properties using the probability model associated with randomly grown binary search trees leads to wave equations. We use a "normalized" integral equation as a pattern to model a specific wave equation and investigate the asymptotic behavior of its solution. This methodology is applied to some particular cases of recurrent properties like testing equality, detecting direct occurrences and clashes or pattern matching.
Wydawca
Czasopismo
Rocznik
Tom
Strony
409--439
Opis fizyczny
bibliogr. 42 poz., wykr.
Twórcy
autor
autor
- Department Sistemas Informaticos y Computacion, Facultad CCV. Matematicas, , Universidad Complutense 28040 Madrid, Spain, minesfc@sip.ucm.es
Bibliografia
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- [7] Casas, R., Fernández-Camacho,M. I., Steyaert, J. M.: Algebraic simplification in computer algebra: an analysis of bottom-up algorithms, Theoretical Computer Science, 74(3), 1990, 273-298.
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- [9] Fernández-Camacho, M. I.: Análisis Medio de Algoritmos de Reducción sobre Arboles, PhD. thesis, Universidad Complutense de Madrid, 1988.
- [10] Fill, J. A., Flajolet, P., Kapur, N.: Singularity analysis, Hadamard products and tree recurrences, Journal of Computational and Applied Mathematics, vol. 174, 2005, 271-313.
- [11] Flajolet, P., Odlyzko, A.: Singularity analysis of generating functions, SIAM J. on Discrete Mathematics, vol. 3, No. 2, 1990, 216-240.
- [12] Flajolet, P., Sedgewick, R.: The average case analysis of algorithms: Counting and generating functions, Research Report 1888, INRIA, March 1993.
- [13] Flajolet, P., Sedgewick, R.: The average case analysis of algorithms: Complex asymptotics and generating functions, Research Report 2026, INRIA, September 1993.
- [14] Goulden, I., Jackson, D.: Combinatorial Enumerations, JohnWiley, New York, 1983.
- [15] Gradshteyn, I. S., Ryzhik, I. M.: Table of Integrals, Series and Products, Ed. Academic Press Inc, 1980.
- [16] Gustafson, K. E.: Introduction to Partial Differential Equations and Hilbert Space Methods, John Wiley &Sons, Inc., 2nd Ed., 1987.
- [17] Guzmán, M.: Ecuaciones Diferenciales Ordinarias. Teoría de Estabilidad y Control, Ed. Alhambra, Madrid 1980.
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- [20] Hoffmann, C. M., O'Donnell,M. J.: Pattern matching in trees, Journal of the ACM, vol. 29, No. 1, 1982, 68-95.
- [21] Knessl, C., Szpankowski,W.: The height of a binary search tree: the limiting distribution perspective, Theoretical Computer Science, 289(1), 2002, 649-703.
- [22] Knight, K.: Unification: a multidisciplinary survey, ACM Comp. Surveys 21, 1989, 93-124.
- [23] Knuth, D. E.: The Art of Computer Programming: Sorting and Searching, vol. 3, Addison-Wesley, Reading, MA, 1973.
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- [29] Martínez, C., Panholzer, A., Prodinger, H.: Partial match queries in relaxed multidimensional search trees, Algorithmica 29(1), 2001, 181-204.
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- [35] Sánchez-Couso, J. R., Fernández-Camacho, M. I.: Reductions in binary search trees, Theoretical Computer Science, 355(3), 2006, 327-353.
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- [37] Steyaert, J. M.: Structure et Complexité des Algorithmes, PhD. thesis, Université Paris, April 1984.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0014-0049