메뉴 건너뛰기




Volumn 174, Issue 2, 2005, Pages 271-313

Singularity analysis, Hadamard products, and tree recurrences

Author keywords

Asymptotic expansions; Contour integration; Divide and conquer; Generalized polylogarithm; Generating functions; Hadamard products; Moment pumping; Shape functional; Singularity analysis; Tree recurrences

Indexed keywords

ALGORITHMS; DIFFERENTIATION (CALCULUS); INTEGRATION; MATHEMATICAL MODELS; TREES (MATHEMATICS);

EID: 11044235781     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.04.014     Document Type: Article
Times cited : (53)

References (63)
  • 1
    • 0004245694 scopus 로고
    • Dover New York (a reprint of the tenth National Bureau of Standards edition, 1964)
    • M. Abramowitz I.A. Stegun Handbook of Mathematical Functions 1973 Dover New York (a reprint of the tenth National Bureau of Standards edition, 1964)
    • (1973) Handbook of Mathematical Functions
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 84987515604 scopus 로고
    • Varieties of increasing trees
    • J.-C. Raoult (Ed.) Proceedings of the 17th Colloquium on Trees in Algebra and Programming, Rennes, France, February
    • F. Bergeron, P. Flajolet, B. Salvy, Varieties of increasing trees, in: J.-C. Raoult (Ed.), CAAP'92, Lecture Notes in Computer Science, Vol. 581, Proceedings of the 17th Colloquium on Trees in Algebra and Programming, Rennes, France, February 1992, pp. 24-48.
    • (1992) CAAP'92, Lecture Notes in Computer Science , vol.581 , pp. 24-48
    • Bergeron, F.1    Flajolet, P.2    Salvy, B.3
  • 4
    • 0004057603 scopus 로고
    • Leipzig: Teubner. Two vols, (Reprinted by Johnson, New York, 1968)
    • L. Bieberbach Lehrbuch der Funktionen Theorie, Two vols. 1931 Teubner Leipzig (Reprinted by Johnson, New York, 1968)
    • (1931) Lehrbuch Der Funktionen Theorie
    • Bieberbach, L.1
  • 6
    • 0035539863 scopus 로고    scopus 로고
    • Phase changes in random m-ary search trees and generalized quicksort
    • H.-H. Chern H.-K. Hwang Phase changes in random m-ary search trees and generalized quicksort Random Struct. Algorithms 19 3-4 2001 316-358
    • (2001) Random Struct. Algorithms , vol.19 , Issue.3-4 , pp. 316-358
    • Chern, H.-H.1    Hwang, H.-K.2
  • 7
    • 0036660151 scopus 로고    scopus 로고
    • An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms
    • analysis of algorithms
    • H.-H. Chern H.-K. Hwang T.-H. Tsai An asymptotic theory for Cauchy-Euler differential equations with applications to the analysis of algorithms J. Algorithms 44 1 2002 177-225 analysis of algorithms
    • (2002) J. Algorithms , vol.44 , Issue.1 , pp. 177-225
    • Chern, H.-H.1    Hwang, H.-K.2    Tsai, T.-H.3
  • 8
    • 11044224965 scopus 로고    scopus 로고
    • Staircase polygons, a simplified model for self-avoiding walks
    • published electronically by Algorithms Project, INRIA
    • F. Chyzak Staircase polygons, a simplified model for self-avoiding walks Stud. Automat. Combin. I 1997 26 published electronically by Algorithms Project, INRIA
    • (1997) Stud. Automat. Combin. I , pp. 26
    • Chyzak, F.1
  • 12
    • 0037119018 scopus 로고    scopus 로고
    • Phase transition in a random fragmentation problem with applications to computer science
    • D.S. Dean S.N. Majumdar Phase transition in a random fragmentation problem with applications to computer science J. Phys. A Math. Gen. 35 2002 L501-L507
    • (2002) J. Phys. A Math. Gen. , vol.35
    • Dean, D.S.1    Majumdar, S.N.2
  • 13
    • 11044233431 scopus 로고    scopus 로고
    • Asymptotic analysis of binomial recurrences
    • Fields Inst. Commun. American Mathematical Society, Providence, RI
    • G. Derfel, F. Vogl, Asymptotic analysis of binomial recurrences, in: Topics in Functional Differential and Difference Equations (Lisbon, 1999), Fields Inst. Commun., Vol. 29, American Mathematical Society, Providence, RI, 2001, pp. 93-104.
    • (2201) Topics in Functional Differential and Difference Equations (Lisbon, 1999) , vol.29 , pp. 93-104
    • Derfel, G.1    Vogl, F.2
  • 14
    • 0004043328 scopus 로고
    • New York: Dover. (a reprint of the first Oxford University Press edition, 1931)
    • P. Dienes The Taylor Series 1958 Dover New York (a reprint of the first Oxford University Press edition, 1931)
    • (1958) The Taylor Series
    • Dienes, P.1
  • 16
    • 0030304083 scopus 로고    scopus 로고
    • On the distribution of binary search trees under the random permutation model
    • J.A. Fill On the distribution of binary search trees under the random permutation model Random Struct. Algorithms 8 1 1996 1-25
    • (1996) Random Struct. Algorithms , vol.8 , Issue.1 , pp. 1-25
    • Fill, J.A.1
  • 17
    • 11044224359 scopus 로고    scopus 로고
    • An invariance principle for simply generated families of trees
    • Technical Report, Department of Mathematical Sciences, The Johns Hopkins University
    • J.A. Fill, N. Kapur, An invariance principle for simply generated families of trees, Technical Report, Department of Mathematical Sciences, The Johns Hopkins University, 2003.
    • (2003)
    • Fill, J.A.1    Kapur, N.2
  • 18
    • 5144220595 scopus 로고    scopus 로고
    • Limiting distributions of additive functionals on Catalan trees
    • to appear
    • J.A. Fill, N. Kapur, Limiting distributions of additive functionals on Catalan trees, Theor. Comput. Sci. (2004), to appear.
    • (2004) Theor. Comput. Sci.
    • Fill, J.A.1    Kapur, N.2
  • 19
    • 1542312122 scopus 로고    scopus 로고
    • Transfer theorems and asymptotic distributional results for m-ary search trees
    • submitted for publication, arXiv:math.PR/0306050
    • J.A. Fill, N. Kapur, Transfer theorems and asymptotic distributional results for m-ary search trees, 2003, submitted for publication, arXiv:mAth.PR/0306050.
    • (2003)
    • Fill, J.A.1    Kapur, N.2
  • 21
    • 0007554179 scopus 로고    scopus 로고
    • Singularity analysis and asymptotics of Bernoulli sums
    • P. Flajolet Singularity analysis and asymptotics of Bernoulli sums Theoret. Comput. Sci. 215 1-2 1999 371-381
    • (1999) Theoret. Comput. Sci. , vol.215 , Issue.1-2 , pp. 371-381
    • Flajolet, P.1
  • 22
    • 21844484375 scopus 로고
    • Mellin transforms and asymptotics: The mergesort recurrence
    • P. Flajolet M. Golin Mellin transforms and asymptotics: The mergesort recurrence Acta Inform. 31 1994 673-696
    • (1994) Acta Inform. , vol.31 , pp. 673-696
    • Flajolet, P.1    Golin, M.2
  • 25
    • 19544388116 scopus 로고    scopus 로고
    • On the analysis of linear probing hashing
    • P. Flajolet P. Poblete A. Viola On the analysis of linear probing hashing Algorithmica 22 4 1998 490-515
    • (1998) Algorithmica , vol.22 , Issue.4 , pp. 490-515
    • Flajolet, P.1    Poblete, P.2    Viola, A.3
  • 26
    • 0022698404 scopus 로고
    • Partial match retrieval of multidimensional data
    • P. Flajolet C. Puech Partial match retrieval of multidimensional data J. ACM 33 2 1986 371-407
    • (1986) J. ACM , vol.33 , Issue.2 , pp. 371-407
    • Flajolet, P.1    Puech, C.2
  • 27
    • 84990661907 scopus 로고
    • Generalized digital trees and their difference - Differential equations
    • P. Flajolet B. Richmond Generalized digital trees and their difference - differential equations Random Struct. Algorithms 3 3 1992 305-320
    • (1992) Random Struct. Algorithms , vol.3 , Issue.3 , pp. 305-320
    • Flajolet, P.1    Richmond, B.2
  • 28
    • 5144219752 scopus 로고
    • A complexity calculus for recursive tree algorithms
    • P. Flajolet J.-M. Steyaert A complexity calculus for recursive tree algorithms Math. Systems Theory 19 1987 301-331
    • (1987) Math. Systems Theory , vol.19 , pp. 301-331
    • Flajolet, P.1    Steyaert, J.-M.2
  • 29
    • 0005199205 scopus 로고
    • A Watson sum for a cubic lattice
    • M.L. Glasser A Watson sum for a cubic lattice J. Math. Phys. 13 1972 1145-1146
    • (1972) J. Math. Phys. , vol.13 , pp. 1145-1146
    • Glasser, M.L.1
  • 32
    • 0011630495 scopus 로고
    • Staircase polygons, elliptic integrals, heun functions, and lattice green functions
    • A.J. Guttmann T. Prellberg Staircase polygons, elliptic integrals, heun functions, and lattice green functions Phys. Rev. E 47 4 1993 R2233-2236
    • (1993) Phys. Rev. E , vol.47 , Issue.4
    • Guttmann, A.J.1    Prellberg, T.2
  • 36
    • 0010836626 scopus 로고
    • Page usage in a quadtree index
    • M. Hoshi P. Flajolet Page usage in a quadtree index BIT 32 1992 384-402
    • (1992) BIT , vol.32 , pp. 384-402
    • Hoshi, M.1    Flajolet, P.2
  • 37
    • 0036766889 scopus 로고    scopus 로고
    • Phase change of limit laws in the quicksort recurrence under varying toll functions
    • electronic
    • H.-K. Hwang R. Neininger Phase change of limit laws in the quicksort recurrence under varying toll functions SIAM J. Comput. 31 6 2002 1687-1722 electronic
    • (2002) SIAM J. Comput. , vol.31 , Issue.6 , pp. 1687-1722
    • Hwang, H.-K.1    Neininger, R.2
  • 38
    • 11044223550 scopus 로고    scopus 로고
    • Additive functionals on random search trees
    • Ph.D. Thesis, Department of Mathematical Sciences, The Johns Hopkins University, April
    • N. Kapur, Additive functionals on random search trees, Ph.D. Thesis, Department of Mathematical Sciences, The Johns Hopkins University, April 2003.
    • (2003)
    • Kapur, N.1
  • 39
    • 0003657590 scopus 로고    scopus 로고
    • 3rd Edition, Fundamental Algorithms Addison-Wesley, Reading, MA
    • D.E. Knuth, The Art of Computer Programming, 3rd Edition, Fundamental Algorithms, Vol. 1, Addison-Wesley, Reading, MA, 1997.
    • (1997) The Art of Computer Programming , vol.1
    • Knuth, D.E.1
  • 40
    • 0003657590 scopus 로고    scopus 로고
    • 2nd Edition, Sorting and Searching, Reading, MA: Addison-Wesley
    • D.E. Knuth The Art of Computer Programming, 2nd Edition, Sorting and Searching, Vol. 3 1998 Addison-Wesley Reading, MA
    • (1998) The Art of Computer Programming , vol.3
    • Knuth, D.E.1
  • 42
    • 84966223881 scopus 로고
    • A recurrence related to trees
    • D.E. Knuth B. Pittel A recurrence related to trees Proc. Amer. Math. Soc. 105 2 1989 335-349
    • (1989) Proc. Amer. Math. Soc. , vol.105 , Issue.2 , pp. 335-349
    • Knuth, D.E.1    Pittel, B.2
  • 43
    • 0000789133 scopus 로고
    • The expected linearity of a simple equivalence algorithm
    • D.E. Knuth A. Schönhage The expected linearity of a simple equivalence algorithm Theoret. Comput. Sci. 6 1978 281-315
    • (1978) Theoret. Comput. Sci. , vol.6 , pp. 281-315
    • Knuth, D.E.1    Schönhage, A.2
  • 45
    • 0021625402 scopus 로고
    • The Brownian excursion: A numerical analysis
    • G. Louchard The Brownian excursion: A numerical analysis Comput. Math. Appl. 10 6 1984 413-417
    • (1984) Comput. Math. Appl. , vol.10 , Issue.6 , pp. 413-417
    • Louchard, G.1
  • 49
    • 0001270611 scopus 로고
    • On the altitude of nodes in random trees
    • A. Meir J.W. Moon On the altitude of nodes in random trees Canad. J. Math. 30 1978 997-1015
    • (1978) Canad. J. Math. , vol.30 , pp. 997-1015
    • Meir, A.1    Moon, J.W.2
  • 50
    • 0036566412 scopus 로고    scopus 로고
    • On binary search tree recursions with monomials as toll functions
    • R. Neininger On binary search tree recursions with monomials as toll functions J. Comput. Appl. Math. 142 1 2002 185-196
    • (2002) J. Comput. Appl. Math. , vol.142 , Issue.1 , pp. 185-196
    • Neininger, R.1
  • 51
    • 0000278117 scopus 로고
    • Asymptotic enumeration methods
    • R. Graham M. Grötschel L. Lovász Elsevier Amsterdam
    • A.M. Odlyzko Asymptotic enumeration methods in: R. Graham M. Grötschel L. Lovász Handbook of Combinatorics, Vol. II 1995 Elsevier Amsterdam 1063-1229
    • (1995) Handbook of Combinatorics , vol.2 , pp. 1063-1229
    • Odlyzko, A.M.1
  • 53
    • 0033267675 scopus 로고    scopus 로고
    • Normal convergence problem? Two moments and a recurrence may be the clues
    • B. Pittel Normal convergence problem? Two moments and a recurrence may be the clues Ann. Appl. Probab. 9 4 1999 1260-1302
    • (1999) Ann. Appl. Probab. , vol.9 , Issue.4 , pp. 1260-1302
    • Pittel, B.1
  • 54
    • 0002015483 scopus 로고    scopus 로고
    • The contraction method for recursive algorithms
    • U. Rösler L. Rüschendorf The contraction method for recursive algorithms Algorithmica 29 1/2 2001 3-33
    • (2001) Algorithmica , vol.29 , Issue.1-2 , pp. 3-33
    • Rösler, U.1    Rüschendorf, L.2
  • 55
    • 84951189828 scopus 로고    scopus 로고
    • An improved master theorem for divide-and-conquer recurrences
    • Springer Berlin
    • S. Roura An improved master theorem for divide-and-conquer recurrences Automata Languages and Programming (Bologna, 1997) 1997 Springer Berlin 449-459
    • (1997) Automata Languages and Programming (Bologna, 1997) , pp. 449-459
    • Roura, S.1
  • 56
    • 0004045951 scopus 로고
    • Asymptotique automatique et fonctions génératrices
    • Ph.D. Thesis, École Polytechnique
    • B. Salvy, Asymptotique automatique et fonctions génératrices, Ph.D. Thesis, École Polytechnique, 1991.
    • (1991)
    • Salvy, B.1
  • 57
    • 0004112038 scopus 로고
    • 2nd Edition 1988, Reading, MA: Addison-Wesley
    • R. Sedgewick Algorithms 2nd Edition 1988 Addison-Wesley Reading, MA
    • (1988) Algorithms
    • Sedgewick, R.1
  • 59
  • 61
    • 0007553418 scopus 로고
    • On a probability problem connected with railway traffic
    • L. Takács On a probability problem connected with railway traffic J. Appl. Math. Stochastic Anal. 4 1 1991 1-27
    • (1991) J. Appl. Math. Stochastic Anal. , vol.4 , Issue.1 , pp. 1-27
    • Takács, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.