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Volumn 18, Issue 1, 2008, Pages 288-333

A functional limit theorem for the profile of search trees

Author keywords

Analysis of algorithms; Functional limit theorem; Profile of trees; Random trees; Search trees

Indexed keywords


EID: 51349156960     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/07-AAP457     Document Type: Article
Times cited : (40)

References (36)
  • 1
    • 53349179421 scopus 로고    scopus 로고
    • BENTKUS, YU. V. and RACHKAUSKAS, A. (1984). Estimates for the distance between sums of independent random elements in Banach spaces. Teor. Veroyatnost. i Primenen. 29 49-64.
    • BENTKUS, YU. V. and RACHKAUSKAS, A. (1984). Estimates for the distance between sums of independent random elements in Banach spaces. Teor. Veroyatnost. i Primenen. 29 49-64.
  • 2
    • 53349147728 scopus 로고    scopus 로고
    • [English transl. Theory Probab. Appl. (1984) 50-65.] MR0739500
    • [English transl. Theory Probab. Appl. (1984) 50-65.] MR0739500
  • 3
    • 53349162850 scopus 로고    scopus 로고
    • BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York. MR0233396
    • BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York. MR0233396
  • 4
    • 33750513585 scopus 로고    scopus 로고
    • The density of the ISE and local limit laws for embedded trees
    • MR2260075
    • BOUSQUET-MÉLOU, M. and JANSON, S. (2006). The density of the ISE and local limit laws for embedded trees. Ann. Appl. Probab. 16 1597-1632. MR2260075
    • (2006) Ann. Appl. Probab , vol.16 , pp. 1597-1632
    • BOUSQUET-MÉLOU, M.1    JANSON, S.2
  • 6
    • 33846857300 scopus 로고    scopus 로고
    • The random multisection problem, travelling waves, and the distribution of the height of m-ary search trees
    • MR2291958
    • CHAUVIN, B. and DRMOTA, M. (2006). The random multisection problem, travelling waves, and the distribution of the height of m-ary search trees. Algorithmica 46 299-327. MR2291958
    • (2006) Algorithmica , vol.46 , pp. 299-327
    • CHAUVIN, B.1    DRMOTA, M.2
  • 8
    • 21244502828 scopus 로고    scopus 로고
    • Connecting yule process, bisection and binary search trees via martingales
    • CHAUVIN, B. and ROUAULT, A. (2004). Connecting yule process, bisection and binary search trees via martingales. J.. Iranian Statistical Society 3 89-116.
    • (2004) J.. Iranian Statistical Society , vol.3 , pp. 89-116
    • CHAUVIN, B.1    ROUAULT, A.2
  • 9
    • 0003093351 scopus 로고    scopus 로고
    • CHERN, H.-H. and HWANG, H.-K. (2001). Transitional behaviors of the average cost of Quicksort with median-of-(2t + 1). Algorithmica 29 44-69. MR1887298
    • CHERN, H.-H. and HWANG, H.-K. (2001). Transitional behaviors of the average cost of Quicksort with median-of-(2t + 1). Algorithmica 29 44-69. MR1887298
  • 10
    • 0036660151 scopus 로고    scopus 로고
    • An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms
    • MR1933199
    • CHERN, H.-H., HWANG, H.-K. and TSAI, T.-H. (2002). An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms. J. Algorithms 44 177-225. MR1933199
    • (2002) J. Algorithms , vol.44 , pp. 177-225
    • CHERN, H.-H.1    HWANG, H.-K.2    TSAI, T.-H.3
  • 11
    • 33746925676 scopus 로고    scopus 로고
    • Width and mode of the profile for some random trees of logarithmic height
    • MR2244436
    • DEVROYE, L. and HWANG, H.-K. (2006). Width and mode of the profile for some random trees of logarithmic height. Ann. Appl. Probab. 16 886-918. MR2244436
    • (2006) Ann. Appl. Probab , vol.16 , pp. 886-918
    • DEVROYE, L.1    HWANG, H.-K.2
  • 12
    • 22244487665 scopus 로고    scopus 로고
    • Profiles of random trees: Correlation and width of random recursive trees and binary search trees
    • MR2144556
    • DRMOTA, M. and HWANG, H.-K. (2005). Profiles of random trees: Correlation and width of random recursive trees and binary search trees. Adv. in Appl. Probab. 37 321-341. MR2144556
    • (2005) Adv. in Appl. Probab , vol.37 , pp. 321-341
    • DRMOTA, M.1    HWANG, H.-K.2
  • 13
    • 22244444622 scopus 로고    scopus 로고
    • DRMOTA, M. and HWANG, H.-K. (2005). Bimodality and phase transitions in the profile variance of random binary search trees. SLAM J. Discrete Math. 19 19-45. MR2178182
    • DRMOTA, M. and HWANG, H.-K. (2005). Bimodality and phase transitions in the profile variance of random binary search trees. SLAM J. Discrete Math. 19 19-45. MR2178182
  • 14
    • 0000640693 scopus 로고
    • Singularity analysis of generating functions
    • MR1039294
    • FLAJOLET, P. and ODLYZKO, A. (1990). Singularity analysis of generating functions. SIAM J. Discrete Math. 3 216-240. MR1039294
    • (1990) SIAM J. Discrete Math , vol.3 , pp. 216-240
    • FLAJOLET, P.1    ODLYZKO, A.2
  • 15
    • 84925121989 scopus 로고    scopus 로고
    • Cambridge Univ. Press. To appear. Available at
    • FLAJOLET, P. and SEDGEWICK, R. (2008). Analytic Combinatorics. Cambridge Univ. Press. To appear. Available at http://algo.inria.fr/flajolet/Publications/books.html.
    • (2008) Analytic Combinatorics
    • FLAJOLET, P.1    SEDGEWICK, R.2
  • 16
    • 33846883721 scopus 로고    scopus 로고
    • Profiles of random trees: Limit theorems for random recursive trees and binary search trees
    • MR2291961
    • FUCHS, M., HWANG, H.-K. and NEININGER, R. (2006). Profiles of random trees: Limit theorems for random recursive trees and binary search trees. Algorithmica 46 367-407. MR2291961
    • (2006) Algorithmica , vol.46 , pp. 367-407
    • FUCHS, M.1    HWANG, H.-K.2    NEININGER, R.3
  • 17
    • 53349165028 scopus 로고
    • On the central limit theorem in Hilbert space
    • MR0573725
    • GINÉ, E. and LEÓN, J. R. (1980). On the central limit theorem in Hilbert space. Stochastica 4 43-71. MR0573725
    • (1980) Stochastica , vol.4 , pp. 43-71
    • GINÉ, E.1    LEÓN, J.R.2
  • 18
    • 34247466528 scopus 로고    scopus 로고
    • Profiles of random trees: Plane-oriented recursive trees
    • MR2309623
    • HWANG, H.-K. (2007). Profiles of random trees: Plane-oriented recursive trees. Random Structures Algorithms 30 380-413. MR2309623
    • (2007) Random Structures Algorithms , vol.30 , pp. 380-413
    • HWANG, H.-K.1
  • 19
    • 53349147719 scopus 로고    scopus 로고
    • JACOD, J. and SHIRYAEV, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin. MR0959133
    • JACOD, J. and SHIRYAEV, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin. MR0959133
  • 20
    • 53349167908 scopus 로고    scopus 로고
    • JANSON, S. (1994). Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics. Amer. Math. Soc., Providence, RI. MR1219708
    • JANSON, S. (1994). Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics. Amer. Math. Soc., Providence, RI. MR1219708
  • 21
    • 53349167905 scopus 로고    scopus 로고
    • JOHNSON, N. L. and KOTZ, S. (1977). Urn Models and Their Applications. Wiley, New York. MR0488211
    • JOHNSON, N. L. and KOTZ, S. (1977). Urn Models and Their Applications. Wiley, New York. MR0488211
  • 22
    • 53349147189 scopus 로고    scopus 로고
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd ed. Springer, New York. MR1876169
  • 23
    • 53349180057 scopus 로고    scopus 로고
    • KRANTZ, S. G. (1982). Function Theory of Several Complex Variables. Wiley, New York, 1982. MR0635928
    • KRANTZ, S. G. (1982). Function Theory of Several Complex Variables. Wiley, New York, 1982. MR0635928
  • 24
    • 53349180058 scopus 로고    scopus 로고
    • LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces. Isoperimetry and Processes. Springer, Berlin. MR1102015
    • LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces. Isoperimetry and Processes. Springer, Berlin. MR1102015
  • 25
    • 0001407755 scopus 로고
    • Weak convergence of probability measures and random functions in the function space D(0, ∞)
    • MR0362429
    • LINDVALL, T. (1973). Weak convergence of probability measures and random functions in the function space D(0, ∞). J. Appl. Probab. 10 109-121. MR0362429
    • (1973) J. Appl. Probab , vol.10 , pp. 109-121
    • LINDVALL, T.1
  • 26
    • 0001744630 scopus 로고
    • More combinatorial problems on certain trees
    • MR0172492
    • LYNCH, W. (1965). More combinatorial problems on certain trees. Comput. J. 7 299-302. MR0172492
    • (1965) Comput. J , vol.7 , pp. 299-302
    • LYNCH, W.1
  • 27
    • 53349147727 scopus 로고    scopus 로고
    • MAHMOUD, H. M. (1992). Evolution of Random Search Trees. Wiley, New York. MR1140708
    • MAHMOUD, H. M. (1992). Evolution of Random Search Trees. Wiley, New York. MR1140708
  • 28
    • 4544255498 scopus 로고    scopus 로고
    • A general limit theorem for recursive algorithms and combinatorial structures
    • MR2023025
    • NEININGER, R. and RÜSCHENDORF, L. (2004). A general limit theorem for recursive algorithms and combinatorial structures. Ann. Appl. Probab. 14 378-418. MR2023025
    • (2004) Ann. Appl. Probab , vol.14 , pp. 378-418
    • NEININGER, R.1    RÜSCHENDORF, L.2
  • 29
    • 53349178576 scopus 로고    scopus 로고
    • RUDIN, W. (1991). Functional Analysis, 2nd ed. McGraw-Hill, New York. MR1157815
    • RUDIN, W. (1991). Functional Analysis, 2nd ed. McGraw-Hill, New York. MR1157815
  • 30
    • 53349179411 scopus 로고    scopus 로고
    • TRÈVES, F. (1967). Topological Vector Spaces, Distributions and Kernels. Academic Press, New York. MR0225131
    • TRÈVES, F. (1967). Topological Vector Spaces, Distributions and Kernels. Academic Press, New York. MR0225131
  • 31
    • 49749139637 scopus 로고
    • Approximation of the distributions of sums of independent random variables with values in infinite-dimensional spaces
    • ZOLOTAREV, V. M. (1977). Approximation of the distributions of sums of independent random variables with values in infinite-dimensional spaces. Teor. Veroyatnost. i Primenen. 21 741-758.
    • (1977) Teor. Veroyatnost. i Primenen , vol.21 , pp. 741-758
    • ZOLOTAREV, V.M.1
  • 32
    • 53349103693 scopus 로고    scopus 로고
    • [Erratum (1977) 22 901.
    • [Erratum (1977) 22 901.
  • 34
    • 53349165039 scopus 로고    scopus 로고
    • 22 881.] MR0517338
    • (1977) 22 881.] MR0517338
  • 35
    • 1542633980 scopus 로고
    • Ideal metrics in the problem of approximating the distributions of sums of independent random variables
    • ZOLOTAREV, V. M. (1977). Ideal metrics in the problem of approximating the distributions of sums of independent random variables. Teor. Veroyatnost. i Primenen. 22 (1977) 449-465.
    • (1977) Teor. Veroyatnost. i Primenen , vol.22 , pp. 449-465
    • ZOLOTAREV, V.M.1
  • 36
    • 53349162849 scopus 로고    scopus 로고
    • [English transl. Theory Probab. Appl. (1977) 22 433-449.] MR0455066
    • [English transl. Theory Probab. Appl. (1977) 22 433-449.] MR0455066


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