Brownian motion and algorithm complexity

The Brownian motion is shown to be a useful tool in analysing some sorting and tree manipulation algorithms.

[1]  Philippe Flajolet,et al.  A Branching Process Arising in Dynamic Hashing, Trie Searching and Polynomial Factorization , 1982, ICALP.

[2]  Kai Lai Chung,et al.  Excursions in Brownian motion , 1976 .

[3]  Frank B. Knight,et al.  On the excursion process of Brownian motion , 1980 .

[4]  Guy Louchard,et al.  KAC'S FORMULA, LEVY'S LOCAL TIME AND BROWNIAN EXCURSION , 1984 .

[5]  Robert Sedgewick Data Movement in Odd-Even Merging , 1978, SIAM J. Comput..

[6]  Philippe Flajolet,et al.  The analysis of simple list structures , 1986, Inf. Sci..

[7]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[8]  Jean Françon,et al.  Sur Le Nombre de Registres Nécessaires a L'évaluation D'une Expression Arithmétique , 1984, RAIRO Theor. Informatics Appl..

[9]  Philippe Flajolet,et al.  A Note on Gray Code and Odd-Even Merge , 1980, SIAM J. Comput..

[10]  Robert Cori,et al.  Une Preuve Combinatiore de la Rationalité d'une Série Génératrice Associée aux Arbres , 1982, RAIRO - Theoretical Informatics and Applications.

[11]  Philippe Flajolet,et al.  Analyse d'algorithmes de manipulation d'arbres et de fichiers , 1981 .

[12]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[13]  L. Shepp,et al.  On the integral of the absolute value of the pinned Wiener process-calculation of its probability de , 1982 .

[14]  M. Kac On Deviations between Theoretical and Empirical Distributions. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[15]  G. Louchard The brownian excursion area: a numerical analysis , 1984 .

[16]  Guy Louchard,et al.  The Brownian Motion: A Neglected Tool for the Complexity Analysis of Sorted Tables Manipulation , 1983, RAIRO Theor. Informatics Appl..

[17]  Philippe Flajolet,et al.  The Average Height of Binary Trees and Other Simple Trees , 1982, J. Comput. Syst. Sci..

[18]  Philippe Flajolet Combinatorial aspects of continued fractions , 1980, Discret. Math..

[19]  Helmut Prodinger,et al.  Register Allocation for Unary-Binary Trees , 1986, SIAM J. Comput..

[20]  A. Rényi,et al.  On the height of trees , 1967, Journal of the Australian Mathematical Society.

[21]  W. D. Kaigh An Invariance Principle for Random Walk Conditioned by a Late Return to Zero , 1976 .

[22]  Robert Sedgewick Mathematical analysis of combinatorial algorithms , 1983 .