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Volumn 19, Issue 3-4, 2001, Pages 498-524

On a multivariate contraction method for random recursive structures with applications to quicksort

Author keywords

Analysis of algorithms; Contraction method; Median of (2t + 1); Multivariate limit law; Quicksort

Indexed keywords


EID: 0035539864     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.10010     Document Type: Article
Times cited : (51)

References (51)
  • 1
    • 0001183529 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration. II. Multivariate generating functions
    • E.A. Bender and L.B. Richmond, Central and local limit theorems applied to asymptotic enumeration. II. Multivariate generating functions, J Combin Theory Ser, A 34 (1983), 255-265.
    • (1983) J Combin Theory Ser, A , vol.34 , pp. 255-265
    • Bender, E.A.1    Richmond, L.B.2
  • 2
    • 0000485156 scopus 로고
    • Some asymptotic theory for the bootstrap
    • P.J. Bickel and P.A. Freedman, Some asymptotic theory for the bootstrap, Ann Statist 9 (1981), 1196-1217.
    • (1981) Ann Statist , vol.9 , pp. 1196-1217
    • Bickel, P.J.1    Freedman, P.A.2
  • 4
    • 21844519315 scopus 로고
    • 2 convergence theorem for random affine mappings
    • 2 convergence theorem for random affine mappings, J Appl Prohab 32 (1995), 183-192.
    • (1995) J Appl Prohab , vol.32 , pp. 183-192
    • Burton, R.1    Rösler, U.2
  • 5
    • 0003093351 scopus 로고    scopus 로고
    • Transitional behaviors of the average cost of Quicksort with median-of-(2t + 1)
    • H.-H. Chern and H.-K. Hwang, Transitional behaviors of the average cost of Quicksort with median-of-(2t + 1), Algorithmica 29 (2001), 44-69.
    • (2001) Algorithmica , vol.29 , pp. 44-69
    • Chern, H.-H.1    Hwang, H.-K.2
  • 6
    • 0035337493 scopus 로고    scopus 로고
    • Convergence of two-dimensional branching recursions
    • M. Cramer and L. Rüschendorf, Convergence of two-dimensional branching recursions, J Comput Appl Math 130 (2001), 53-73.
    • (2001) J Comput Appl Math , vol.130 , pp. 53-73
    • Cramer, M.1    Rüschendorf, L.2
  • 7
    • 0002630652 scopus 로고
    • Sugli estremi dei momenti delle funzioni di ripartizione doppia
    • G. Dall'Aglio, Sugli estremi dei momenti delle funzioni di ripartizione doppia, Ann Scuoloa Norm Sup Pisa 10 (3) (1956), 35-74.
    • (1956) Ann Scuoloa Norm Sup Pisa , vol.10 , Issue.3 , pp. 35-74
    • Dall'Aglio, G.1
  • 8
    • 0242337623 scopus 로고    scopus 로고
    • Branching processes and their applications in the analysis of tree structures and tree algorithms
    • Springer, Berlin
    • L. Devroye, "Branching processes and their applications in the analysis of tree structures and tree algorithms," Probabilistic methods for algorithmic discrete mathematics, Springer, Berlin, 1998, pp. 249-314.
    • (1998) Probabilistic Methods for Algorithmic Discrete Mathematics , pp. 249-314
    • Devroye, L.1
  • 9
    • 0032107999 scopus 로고    scopus 로고
    • Universal limit laws for the depths in random trees
    • L. Devroye, Universal limit laws for the depths in random trees, SIAM J Comput 28 (1998), 409-432.
    • (1998) SIAM J Comput , vol.28 , pp. 409-432
    • Devroye, L.1
  • 10
    • 0025503037 scopus 로고
    • An analysis of random d-dimensional quad trees
    • L. Devroye and L. Laforest, An analysis of random d-dimensional quad trees, SIAM J Comput 19 (1990), 821-832.
    • (1990) SIAM J Comput , vol.19 , pp. 821-832
    • Devroye, L.1    Laforest, L.2
  • 11
    • 0001258015 scopus 로고    scopus 로고
    • Large deviations for Quicksort
    • C.J.H. McDiarmid and R.B. Hayward, Large deviations for Quicksort, J Algorithms 21 (1996), 476-507.
    • (1996) J Algorithms , vol.21 , pp. 476-507
    • McDiarmid, C.J.H.1    Hayward, R.B.2
  • 12
    • 0014849316 scopus 로고
    • Increasing the efficiency of quicksort
    • M.H. van Emden, Increasing the efficiency of quicksort, Commun ACM 13 (1970), 563-567.
    • (1970) Commun ACM , vol.13 , pp. 563-567
    • Van Emden, M.H.1
  • 13
    • 0016353777 scopus 로고
    • Quad trees, a data structure for retrieval on composite keys
    • R. Finkel and J. Bentley, Quad trees, a data structure for retrieval on composite keys Acta Inform 4 (1974), 1-9.
    • (1974) Acta Inform , vol.4 , pp. 1-9
    • Finkel, R.1    Bentley, J.2
  • 16
    • 51249165896 scopus 로고
    • Search costs in quadtrees and singularity perturbation asymptotics
    • P. Flajolet and T. Lafforgue, Search costs in quadtrees and singularity perturbation asymptotics, Discrete Comput Geom 12 (1994), 151-175.
    • (1994) Discrete Comput Geom , vol.12 , pp. 151-175
    • Flajolet, P.1    Lafforgue, T.2
  • 17
    • 0022698404 scopus 로고
    • Partial match retrieval of multidimensional data
    • P. Flajolet and C. Puech, Partial match retrieval of multidimensional data, J ACM 33 (1986), 371-407.
    • (1986) J ACM , vol.33 , pp. 371-407
    • Flajolet, P.1    Puech, C.2
  • 18
    • 38049026666 scopus 로고
    • Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions
    • Z. Gao and L.B. Richmond, Central and local limit theorems applied to asymptotic enumeration. IV. Multivariate generating functions, J Comput Appl Math 41 (1992), 177-186.
    • (1992) J Comput Appl Math , vol.41 , pp. 177-186
    • Gao, Z.1    Richmond, L.B.2
  • 19
    • 0007554189 scopus 로고    scopus 로고
    • A new proof of Yaglom's exponential limit law
    • Birkhäuser, Basel
    • J. Geiger, "A new proof of Yaglom's exponential limit law," Mathematics and computer science (Versailles), Birkhäuser, Basel, 2000, pp. 245-249.
    • (2000) Mathematics and Computer Science (Versailles) , pp. 245-249
    • Geiger, J.1
  • 22
    • 0000975791 scopus 로고
    • Combinatorial analysis of quicksort algorithm
    • P. Hennequin, Combinatorial analysis of quicksort algorithm, RAIRO Inform Théor Appl 23 (1989), 317-333.
    • (1989) RAIRO Inform Théor Appl , vol.23 , pp. 317-333
    • Hennequin, P.1
  • 24
    • 0015009076 scopus 로고
    • On the probability distribution of the values of binary trees
    • H. Hurwitz, Jr., On the probability distribution of the values of binary trees. Comm ACM 14 (1971), 99-102.
    • (1971) Comm ACM , vol.14 , pp. 99-102
    • Hurwitz H., Jr.1
  • 26
    • 0028516486 scopus 로고
    • The joint distribution of elastic buckets in multiway search trees
    • W. Lew and H.M. Mahmoud, The joint distribution of elastic buckets in multiway search trees, SIAM J Comput 23 (1994), 1050-1074.
    • (1994) SIAM J Comput , vol.23 , pp. 1050-1074
    • Lew, W.1    Mahmoud, H.M.2
  • 29
    • 0024052986 scopus 로고
    • On the joint distribution of the insertion path length and the number of comparisons in search trees
    • H.M. Mahmoud and B. Pittel, On the joint distribution of the insertion path length and the number of comparisons in search trees, Discrete Appl Math 20 (1988), 243-251.
    • (1988) Discrete Appl Math , vol.20 , pp. 243-251
    • Mahmoud, H.M.1    Pittel, B.2
  • 30
    • 84990634444 scopus 로고
    • Asymptotic joint normality of outdegrees of nodes in random recursive trees
    • H.M. Mahmoud and R.T. Smythe, Asymptotic joint normality of outdegrees of nodes in random recursive trees, Random Structures Algorithms 3 (1992), 255-266.
    • (1992) Random Structures Algorithms , vol.3 , pp. 255-266
    • Mahmoud, H.M.1    Smythe, R.T.2
  • 31
    • 84990634414 scopus 로고
    • On the structure of random plane-oriented recursive trees and their branches
    • H.M. Mahmoud, R.T Smythe, and J. Szymański, On the structure of random plane-oriented recursive trees and their branches, Random Structures Algorithms 4 (1993), 151-176.
    • (1993) Random Structures Algorithms , vol.4 , pp. 151-176
    • Mahmoud, H.M.1    Smythe, R.T.2    Szymański, J.3
  • 32
    • 0000541715 scopus 로고
    • On the invariance principle for sums of independent identically distributed random variables
    • P. Major, On the invariance principle for sums of independent identically distributed random variables, J Multivariate Anal 8 (1978), 487-517.
    • (1978) J Multivariate Anal , vol.8 , pp. 487-517
    • Major, P.1
  • 33
    • 0036308985 scopus 로고    scopus 로고
    • Optimal sampling strategies in Quicksort and Quickselect
    • to appear
    • C. Martínez and S. Roura, Optimal sampling strategies in Quicksort and Quickselect, SIAM J Comput, to appear.
    • SIAM J Comput
    • Martínez, C.1    Roura, S.2
  • 35
    • 0034359738 scopus 로고    scopus 로고
    • Asymptotic distributions for partial match queries in K-d trees
    • R. Neininger, Asymptotic distributions for partial match queries in K-d trees, Random Structures Algorithms 17 (2000), 403-427.
    • (2000) Random Structures Algorithms , vol.17 , pp. 403-427
    • Neininger, R.1
  • 37
    • 0039346499 scopus 로고    scopus 로고
    • On the internal path length of d-dimensional quad trees
    • R. Neininger and L. Rüschendorf, On the internal path length of d-dimensional quad trees, Random Structures Algorithms 15 (1999), 25-41.
    • (1999) Random Structures Algorithms , vol.15 , pp. 25-41
    • Neininger, R.1    Rüschendorf, L.2
  • 38
    • 0035538467 scopus 로고    scopus 로고
    • Limit laws for partial match queries in quadtrees
    • to appear
    • R. Neininger and L. Rüschendorf, Limit laws for partial match queries in quadtrees Ann Appl Probab, to appear.
    • Ann Appl Probab
    • Neininger, R.1    Rüschendorf, L.2
  • 40
    • 0001131997 scopus 로고
    • Probability metrics and recursive algorithms
    • S.T Rachev and L. Rüschendorf, Probability metrics and recursive algorithms, Adv in Appl Probab 27 (1995), 770-799.
    • (1995) Adv in Appl Probab , vol.27 , pp. 770-799
    • Rachev, S.T.1    Rüschendorf, L.2
  • 42
    • 0002497513 scopus 로고
    • A limiting distribution for quicksort
    • M. Régnier, A limiting distribution for quicksort, RAIRO Inform Théor Appl 23 (1989), 335-343.
    • (1989) RAIRO Inform Théor Appl , vol.23 , pp. 335-343
    • Régnier, M.1
  • 43
    • 0002731988 scopus 로고
    • A limit theorem for "Quicksort,"
    • U. Rösler, A limit theorem for "Quicksort," RAIRO Inform Théor Appl 25 (1991), 85-100.
    • (1991) RAIRO Inform Théor Appl , vol.25 , pp. 85-100
    • Rösler, U.1
  • 44
    • 38249008257 scopus 로고
    • A fixed point theorem for distributions
    • U. Rösler, A fixed point theorem for distributions, Stochastic Process Appl 42 (1992), 195-214.
    • (1992) Stochastic Process Appl , vol.42 , pp. 195-214
    • Rösler, U.1
  • 45
    • 9644259154 scopus 로고    scopus 로고
    • On the analysis of stochastic divide and conquer algorithms
    • U. Rösler, On the analysis of stochastic divide and conquer algorithms, Algorithmica 29 (2001), 238-261.
    • (2001) Algorithmica , vol.29 , pp. 238-261
    • Rösler, U.1
  • 46
    • 0002015483 scopus 로고    scopus 로고
    • The contraction method for recursive algorithms
    • U. Rösler and L. Rüschendorf, The contraction method for recursive algorithms, Algorithmica 29 (2001), 3-33.
    • (2001) Algorithmica , vol.29 , pp. 3-33
    • Rösler, U.1    Rüschendorf, L.2
  • 50
    • 0017427687 scopus 로고
    • The analysis of Quicksort programs
    • R. Sedgewick, The analysis of Quicksort programs, Acta Informat 7 (1977), 327-355.
    • (1977) Acta Informat , vol.7 , pp. 327-355
    • Sedgewick, R.1
  • 51
    • 0003153429 scopus 로고
    • Some properties of a limiting distribution in Quicksort
    • K.H. Tan and P. Hadjicostas, Some properties of a limiting distribution in Quicksort, Statist Probab Lett 25 (1995), 87-94.
    • (1995) Statist Probab Lett , vol.25 , pp. 87-94
    • Tan, K.H.1    Hadjicostas, P.2


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