메뉴 건너뛰기




Volumn 32, Issue 4, 2008, Pages 494-518

The height of increasing trees

Author keywords

Branching process; Height; Increasing tree; Probabilistic analysis; Random tree

Indexed keywords


EID: 52349095614     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20202     Document Type: Article
Times cited : (30)

References (48)
  • 2
    • 0038483826 scopus 로고    scopus 로고
    • Emergence of scaling in random network
    • A. L. Barabási and R. Albert, Emergence of scaling in random network, Science 286 (1999), 509-512.
    • (1999) Science , vol.286 , pp. 509-512
    • Barabási, A.L.1    Albert, R.2
  • 4
    • 0007633320 scopus 로고
    • The first and last-birth problems in a multitype age-dependent branching process
    • J. D. Biggins, The first and last-birth problems in a multitype age-dependent branching process, Adv Appl Probab 8 (1976), 446-459.
    • (1976) Adv Appl Probab , vol.8 , pp. 446-459
    • Biggins, J.D.1
  • 5
    • 0001687281 scopus 로고
    • Chernoff's theorem in the branching random walk
    • J. D. Biggins, Chernoff's theorem in the branching random walk, J Appl Probab 14 (1977), 630-636.
    • (1977) J Appl Probab , vol.14 , pp. 630-636
    • Biggins, J.D.1
  • 6
    • 21244476659 scopus 로고    scopus 로고
    • A note on the growth of random trees
    • J. D. Biggins and D. R. Grey, A note on the growth of random trees, Stat Probab Lett 32 (1997), 339-342.
    • (1997) Stat Probab Lett , vol.32 , pp. 339-342
    • Biggins, J.D.1    Grey, D.R.2
  • 8
    • 33846891340 scopus 로고    scopus 로고
    • Large deviations for the weighted height of an extended class of trees
    • N. Broutin and L. Devroye, Large deviations for the weighted height of an extended class of trees, Algorithmica 46 (2006), 271-297.
    • (2006) Algorithmica , vol.46 , pp. 271-297
    • Broutin, N.1    Devroye, L.2
  • 9
    • 0000182415 scopus 로고
    • A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations
    • H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann Math Stat 23 (1952), 493-507.
    • (1952) Ann Math Stat , vol.23 , pp. 493-507
    • Chernoff, H.1
  • 10
    • 0348150721 scopus 로고
    • File structures using hashing functions
    • E. G. Coffman and J. Eve, File structures using hashing functions, Commun ACM 13 (1970), 427-436.
    • (1970) Commun ACM , vol.13 , pp. 427-436
    • Coffman, E.G.1    Eve, J.2
  • 11
    • 0002178770 scopus 로고
    • Sur un nouveau théorème-limite de la théorie des probabilités
    • Hermann, Paris
    • H. Cramér, Sur un nouveau théorème-limite de la théorie des probabilités. In, Colloque Consacré à la Théorie des Probabilités, volume 736, Hermann, Paris, 1938, pp. 5-23.
    • (1938) Colloque Consacré à la Théorie des Probabilités , vol.736 , pp. 5-23
    • Cramér, H.1
  • 14
    • 0022754664 scopus 로고
    • A note on the height of binary search trees
    • L. Devroye, A note on the height of binary search trees, J ACM 33 (1986), 489-498.
    • (1986) J ACM , vol.33 , pp. 489-498
    • Devroye, L.1
  • 15
    • 0023270968 scopus 로고
    • Branching processes in the analysis of the heights of trees
    • L. Devroye, Branching processes in the analysis of the heights of trees, Acta Inform 24 (1987), 277-298.
    • (1987) Acta Inform , vol.24 , pp. 277-298
    • Devroye, L.1
  • 16
    • 0242337623 scopus 로고    scopus 로고
    • Branching processes and their application in the analysis of tree structures and tree algorithms
    • M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, editors, Probabilistic methods for algorithmic discrete mathematics, of, Springer, Berlin
    • L. Devroye, Branching processes and their application in the analysis of tree structures and tree algorithms, In, M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, editors, Probabilistic methods for algorithmic discrete mathematics, volume 16 of Springer series on algorithms and combinatorics, Springer, Berlin, 1998, pp. 249-314.
    • (1998) Springer series on algorithms and combinatorics , vol.16 , pp. 249-314
    • Devroye, L.1
  • 17
    • 0032107999 scopus 로고    scopus 로고
    • Universal limit laws for depth in random trees
    • L. Devroye, Universal limit laws for depth in random trees, SIAM J Comp 28 (1998), 409-432.
    • (1998) SIAM J Comp , vol.28 , pp. 409-432
    • Devroye, L.1
  • 18
    • 1542666229 scopus 로고    scopus 로고
    • An analytic approach to the height of binary search trees II
    • M. Drmota, An analytic approach to the height of binary search trees II, J ACM 50 (2003), 333-374.
    • (2003) J ACM , vol.50 , pp. 333-374
    • Drmota, M.1
  • 19
    • 52349089785 scopus 로고    scopus 로고
    • M. Drmota, The height of increasing trees, 2006. Annals of Combinatorics, to appear.
    • M. Drmota, The height of increasing trees, 2006. Annals of Combinatorics, to appear.
  • 21
    • 84945709825 scopus 로고
    • Trie memory
    • E. Fredkin, Trie memory, Commun ACM, 3 (1960), 490-499.
    • (1960) Commun ACM , vol.3 , pp. 490-499
    • Fredkin, E.1
  • 25
    • 0001275106 scopus 로고
    • The Gallon-Watson process conditioned on the lolal progeny
    • D. P. Kennedy, The Gallon-Watson process conditioned on the lolal progeny, J Appl Probab 12 (1975), 800-806.
    • (1975) J Appl Probab , vol.12 , pp. 800-806
    • Kennedy, D.P.1
  • 28
    • 0004265775 scopus 로고
    • Optimization Software, New York
    • V. F. Kolchin, Random Mappings, Optimization Software, New York, 1986.
    • (1986) Random Mappings
    • Kolchin, V.F.1
  • 29
    • 0004637325 scopus 로고
    • A note on growing binary trees
    • A. G. Konheim and D. J. Newman, A note on growing binary trees, Discrete Math 4 (1973), 57-63.
    • (1973) Discrete Math , vol.4 , pp. 57-63
    • Konheim, A.G.1    Newman, D.J.2
  • 30
  • 31
    • 0026900464 scopus 로고
    • Distances in plane-oriented recursive trees
    • H. Mahmoud, Distances in plane-oriented recursive trees, J Computat Appl Math 41 (1992), 237-245.
    • (1992) J Computat Appl Math , vol.41 , pp. 237-245
    • Mahmoud, H.1
  • 32
    • 84990634414 scopus 로고
    • On the structure of random plane-oriented recursive trees and their branches
    • H. Mahmoud, R. T. Smythe, and J. Szymanski, On the structure of random plane-oriented recursive trees and their branches, Random Struct Algorithms 4 (1993), 151-176.
    • (1993) Random Struct Algorithms , vol.4 , pp. 151-176
    • Mahmoud, H.1    Smythe, R.T.2    Szymanski, J.3
  • 33
    • 0036308985 scopus 로고    scopus 로고
    • Optimal sampling strategies in quicksort and quickselect
    • C. Martínez and S. Roura, Optimal sampling strategies in quicksort and quickselect, SIAM J Comput 31 (2001), 683-705.
    • (2001) SIAM J Comput , vol.31 , pp. 683-705
    • Martínez, C.1    Roura, S.2
  • 34
    • 0001270611 scopus 로고
    • On the altitude of nodes in random trees
    • A. Meir and J. W. Moon, On the altitude of nodes in random trees, Can J Math 30 (1978), 997-1015.
    • (1978) Can J Math , vol.30 , pp. 997-1015
    • Meir, A.1    Moon, J.W.2
  • 35
    • 0041049688 scopus 로고
    • Counting Labelled Trees, Number 1 in Canadian Mathematical Monographs
    • Montreal
    • J. W. Moon, Counting Labelled Trees, Number 1 in Canadian Mathematical Monographs. Canadian Mathematical Congress, Montreal, 1970.
    • (1970) Canadian Mathematical Congress
    • Moon, J.W.1
  • 36
    • 38149018071 scopus 로고
    • Practical algorithm to retrieve information coded in alphanumeric
    • D. R. Morrison, patricia, Practical algorithm to retrieve information coded in alphanumeric, J ACM 15 (1968), 514-534.
    • (1968) J ACM , vol.15 , pp. 514-534
    • Morrison, D.R.1    patricia2
  • 37
    • 11144294146 scopus 로고    scopus 로고
    • Analysis of some statistics for increasing tree families
    • A. Panholzer and H. Prodinger, Analysis of some statistics for increasing tree families, Discrete Math Theor Comput Sci 6 (2004), 437-460.
    • (2004) Discrete Math Theor Comput Sci , vol.6 , pp. 437-460
    • Panholzer, A.1    Prodinger, H.2
  • 38
    • 34548541183 scopus 로고    scopus 로고
    • The level of nodes in increasing trees revisited
    • A. Panholzer and H. Prodinger, The level of nodes in increasing trees revisited, Random Struct Algorithms 31 (2007), 203-226.
    • (2007) Random Struct Algorithms , vol.31 , pp. 203-226
    • Panholzer, A.1    Prodinger, H.2
  • 39
    • 0021502443 scopus 로고
    • On growing random binary trees
    • B. Pittel, On growing random binary trees, J Math Anal Appl 103 (1984), 461-480.
    • (1984) J Math Anal Appl , vol.103 , pp. 461-480
    • Pittel, B.1
  • 40
    • 0000437595 scopus 로고
    • Asymptotic growth of a class of random trees
    • B. Pittel, Asymptotic growth of a class of random trees, Ann Probab 13 (1985), 414-427.
    • (1985) Ann Probab , vol.13 , pp. 414-427
    • Pittel, B.1
  • 41
    • 84990662431 scopus 로고
    • Note on the height of random recursive trees and m-ary search trees
    • B. Pittel, Note on the height of random recursive trees and m-ary search trees, Random Struct Algorithms 5 (1994), 337-347.
    • (1994) Random Struct Algorithms , vol.5 , pp. 337-347
    • Pittel, B.1
  • 42
    • 0020704386 scopus 로고
    • On monotone functions of tree structures
    • H. Prodinger and F. J. Urbanek, On monotone functions of tree structures, Discrete Appl Math 5 (1983), 222-239.
    • (1983) Discrete Appl Math , vol.5 , pp. 222-239
    • Prodinger, H.1    Urbanek, F.J.2
  • 44
    • 1542456902 scopus 로고    scopus 로고
    • The height of a random binary search tree
    • B. Reed, The height of a random binary search tree, J ACM 50 (2003), 306-332.
    • (2003) J ACM , vol.50 , pp. 306-332
    • Reed, B.1
  • 45
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.1
  • 48
    • 2142846846 scopus 로고    scopus 로고
    • J. Szymański, On a non-uniform random recursive tree, In M. Karoński and Z. Palka, editors, Random Graphs '85, 33 of Annals of Discrete Mathematics, North Holland, 1987, Amsterdam, pp. 297-306.
    • J. Szymański, On a non-uniform random recursive tree, In M. Karoński and Z. Palka, editors, Random Graphs '85, volume 33 of Annals of Discrete Mathematics, North Holland, 1987, Amsterdam, pp. 297-306.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.