Branching Processes and Their Applications in the Analysis of Tree Structures and Tree Algorithms

[1]  Luc Devroye,et al.  On the complexity of branch-and bound search for random trees , 1999 .

[2]  Klaus H. Hinrichs,et al.  Algorithms and data structures - with applications to graphics and geometry , 1999, vdf Lehrbuch.

[3]  Luc Devroye.  Universal Limit Laws for Depths in Random Trees , 1998, SIAM J. Comput..

[4]  D. R. Grey,et al.  A note on the growth of random trees , 1997 .

[5]  J. D. Biggins,et al.  HOW FAST DOES A GENERAL BRANCHING RANDOM WALK SPREAD , 1997 .

[6]  Robin Pemantle,et al.  Random Discrete Structures , 1996 .

[7]  L. Devroye,et al.  Random Minimax Game Trees , 1996 .

[8]  D. Aldous.  PROBABILITY DISTRIBUTIONS ON CLADOGRAMS , 1996 .

[9]  Bruce A. Reed,et al.  On the Variance of the Height of Random Binary Search Trees , 1995, SIAM J. Comput..

[10]  J. Biggins,et al.  The Growth and Spread of the General Branching Random Walk , 1995 .

[11]  Richard M. Karp,et al.  Bounded Branching Process AND/OR Tree Evaluation , 1995, Random Struct. Algorithms.

[12]  Russell Lyons,et al.  Conceptual proofs of L log L criteria for mean behavior of branching processes , 1995 .

[13]  Colin McDiarmid,et al.  Minimal Positions in a Branching Random Walk , 1995 .

[14]  Philippe Flajolet,et al.  Search costs in quadtrees and singularity perturbation asymptotics , 1994, Discret. Comput. Geom..

[15]  Steven Skiena,et al.  Hamilton Triangulations for Fast Rendering , 1994, ESA.

[16]  Hosam M. Mahmoud.  A Strong Law for the Height of Random Binary Pyramids , 1994 .

[17]  Boris G. Pittel,et al.  Note on the Heights of Random Recursive Trees and Random m-ary Search Trees , 1994, Random Struct. Algorithms.

[18]  When does a branching process grow like its mean? Conceptual proofs of L log L criteria , 1994 .

[19]  N. H. Bingham,et al.  Large deviations in the supercritical branching process , 1993, Advances in Applied Probability.

[20]  Jerzy Szymanski,et al.  On the Structure of Random Plane-oriented Recursive Trees and Their Branches , 1993, Random Struct. Algorithms.

[21]  Walter J. Gutjahr,et al.  Expectation Transfer between Branching Processes and Random Trees , 1993, Random Struct. Algorithms.

[22]  Georg Ch. Pflug,et al.  The asymptotic distribution of leaf heights in binary trees , 1992, Graphs Comb..

[23]  H. Mahmoud.  Distances in random plane-oriented recursive trees , 1992 .

[24]  Richard E. Korf,et al.  An Average-Case Analysis of Branch-and-Bound with Applications: Summary of Results , 1992, AAAI.

[25]  G. Pflug,et al.  The asymptotic contour process of a binary tree is a Brownian excursion , 1992 .

[26]  Philippe Flajolet,et al.  Varieties of Increasing Trees , 1992, CAAP.

[27]  Hosam M. Mahmoud,et al.  Evolution of random search trees , 1991, Wiley-Interscience series in discrete mathematics and optimization.

[28]  Georg Ch. Pflug,et al.  The limiting common distribution of two leaf heights in a random brinary tree , 1992, RAIRO Theor. Informatics Appl..

[29]  Walter J. Gutjahr.  The Variance of Level Numbers in Certain Families of Trees , 1992, Random Struct. Algorithms.

[30]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[31]  F. M. Dekking,et al.  Limit distributions for minimal displacement of branching random walks , 1991 .

[32]  Gregory M. Provan,et al.  An Expected-Cost Analysis of Backtracking and Non-Backtracking Algorithms , 1991, IJCAI.

[33]  Gaston H. Gonnet,et al.  The analysis of multidimensional searching in quad-trees , 1991, SODA '91.

[34]  David Aldous,et al.  The Continuum Random Tree III , 1991 .

[35]  D. Aldous.  Stochastic Analysis: The Continuum random tree II: an overview , 1991 .

[36]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity , 1994 .

[37]  R. Durrett.  Probability: Theory and Examples , 1993 .

[38]  Philippe Flajolet,et al.  Average-Case Analysis of Algorithms and Data Structures , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[39]  David Aldous,et al.  The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees , 1990, SIAM J. Discret. Math..

[40]  Luc Devroye,et al.  An Analysis of Random d-Dimensional Quad Trees , 1990, SIAM J. Comput..

[41]  D. R. Woodall.  k-Factors and Neighbourhoods of Independent Sets in Graphs , 1990 .

[42]  Luc Devroye,et al.  On the Height of Random m-ary Search Trees , 1990, Random Struct. Algorithms.

[43]  Xavier Gérard Viennot,et al.  Trees Everywhere , 1990, CAAP.

[44]  Philippe Flajolet,et al.  Singularity Analysis of Generating Functions , 1990, SIAM J. Discret. Math..

[45]  J. Biggins,et al.  The central limit theorem for the supercritical branching random walk, and related results , 1990 .

[46]  Oscar J. Mesa,et al.  Tree-dependent extreme values: the exponential case , 1990, Journal of Applied Probability.

[47]  Richard M. Karp,et al.  The Transitive Closure of a Random Digraph , 1990, Random Struct. Algorithms.

[48]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[49]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[50]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[51]  Maury Bramson,et al.  Statistical Mechanics of Crabgrass , 1989 .

[52]  Jim Pitman,et al.  The branching process in a Brownian excursion , 1989 .

[53]  E. A. Timofeev.  On Finding the Expected Length of a Random Minimal Tree , 1989 .

[54]  P. Meyer,et al.  Séminaire de Probabilités XXIII , 1989 .

[55]  J. -. Gall,et al.  Marches aleatoires, mouvement brownien et processus de branchement , 1989 .

[56]  Hosam M. Mahmoud,et al.  On the joint distribution of the insertion path length and the number of comparisons in search trees , 1988, Discret. Appl. Math..

[57]  D. Aldous,et al.  Two Applications of Urn Processes The Fringe Analysis of Search Trees and The Simulation of Quasi-Stationary Distributions of Markov Chains , 1988, Probability in the Engineering and Informational Sciences.

[58]  B. Derrida,et al.  Polymers on disordered trees, spin glasses, and traveling waves , 1988 .

[59]  Wojciech Szpankowski,et al.  Some Results on V-ary Asymmetric Tries , 1988, J. Algorithms.

[60]  N. H. Bingham,et al.  On the limit of a supercritical branching process , 1988, Journal of Applied Probability.

[61]  David Avis,et al.  Triangulating point sets in space , 1987, Discret. Comput. Geom..

[62]  Guy Louchard.  Exact and Asymptotic Distributions in Digital and Binary Search Trees , 1987, RAIRO Theor. Informatics Appl..

[63]  Philippe Flajolet,et al.  Digital Search Trees Revisited , 1986, SIAM J. Comput..

[64]  Mireille Régnier,et al.  Trie Partitioning Process: Limiting Distributions , 1986, CAAP.

[65]  Harold S. Stone,et al.  The Average Complexity of Depth-First Search with Backtracking and Cutoff , 1986, IBM J. Res. Dev..

[66]  Luc Devroye,et al.  A note on the height of binary search trees , 1986, JACM.

[67]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[68]  B. Pittel.  Paths in a random digital tree: limiting distributions , 1986, Advances in Applied Probability.

[69]  J. Neveu,et al.  Arbres et processus de Galton-Watson , 1986 .

[70]  J. Ian Munro,et al.  The Analysis of a Fringe Heuristic for Binary Search Trees , 1985, J. Algorithms.

[71]  Benjamin W. Wah,et al.  Stochastic Modeling of Branch-and-Bound Algorithms with Best-First Search , 1985, IEEE Transactions on Software Engineering.

[72]  B. Pittel.  Asymptotical Growth of a Class of Random Trees , 1985 .

[73]  E. A. Timofeev.  Random Minimal Trees , 1985 .

[74]  Rainer Kemp,et al.  Fundamentals of the average case analysis of particular algorithms , 1985, Wiley-Teubner series in computer science.

[75]  H. Weiner.  Moments of the maximum in a critical branching process , 1984, Journal of Applied Probability.

[76]  Robert L. Smith,et al.  Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions , 1984, Oper. Res..

[77]  B. Pittel.  On growing random binary trees , 1984 .

[78]  O. Nerman,et al.  The growth and composition of branching populations , 1984, Advances in Applied Probability.

[79]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[80]  Jürg Nievergelt,et al.  The Grid File: An Adaptable, Symmetric Multikey File Structure , 1984, TODS.

[81]  Boris Pittel,et al.  On the Most Probable Shape of a Search Tree Grown from a Random Permutation , 1984 .

[82]  B. Bollobás.  The evolution of random graphs , 1984 .

[83]  Gaston H. Gonnet,et al.  Handbook Of Algorithms And Data Structures , 1984 .

[84]  Douglas R. Smith,et al.  Random Trees and the Analysis of Branch and Bound Procedures , 1984, JACM.

[85]  Svante Janson,et al.  Limit Theorems for Certain Branching Random Walks on Compact Groups and Homogeneous Spaces , 1983 .

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

[87]  Richard M. Karp,et al.  Searching for an Optimal Path in a Tree with Random Costs , 1983, Artif. Intell..

[88]  Paul Walton Purdom,et al.  Search Rearrangement Backtracking and Polynomial Average Time , 1983, Artif. Intell..

[89]  M. Bramson.  Convergence of solutions of the Kolmogorov equation to travelling waves , 1983 .

[90]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[91]  A. Joffe,et al.  Exact distributions of kin numbers in a Galton-Watson process , 1982, Journal of Applied Probability.

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

[93]  R. Y. Rubinstein.  Generating random vectors uniformly distributed inside and on the surface of different regions , 1982 .

[94]  J. Hawkes,et al.  Trees Generated by a Simple Branching Process , 1981 .

[95]  Olle Nerman,et al.  On the convergence of supercritical general (C-M-J) branching processes , 1981 .

[96]  Paul Walton Purdom,et al.  An Average Time Analysis of Backtracking , 1981, SIAM J. Comput..

[97]  Geoffrey Grimmett,et al.  Random labelled trees and their branching networks , 1980 .

[98]  Masaaki Sibuya,et al.  Generalized hypergeometric, digamma and trigamma distributions , 1979 .

[99]  R. Durrett.  Maxima of branching random walks vs. independent random walks , 1979 .

[100]  J. Biggins.  Growth rates in the branching random walk , 1979 .

[101]  John Michael Robson,et al.  The Height of Binary Search Trees , 1979, Aust. Comput. J..

[102]  V. F. Kolchin.  Moment of degeneration of a branching process and height of a random tree , 1978 .

[103]  J. Moon,et al.  On the Altitude of Nodes in Random Trees , 1978, Canadian Journal of Mathematics.

[104]  Maury Bramson,et al.  Maximal displacement of branching brownian motion , 1978 .

[105]  M. Bramson.  Minimal displacement of branching random walk , 1978 .

[106]  J. D. Biggins,et al.  The asymptotic shape of the branching random walk , 1978, Advances in Applied Probability.

[107]  Iosif Pinelis,et al.  Some Inequalities for the Distribution of Sums of Independent Random Variables , 1978 .

[108]  J. Biggins.  Chernoff's theorem in the branching random walk , 1977, Journal of Applied Probability.

[109]  J. Biggins,et al.  Martingale convergence in the branching random walk , 1977, Journal of Applied Probability.

[110]  E. Reingold,et al.  Combinatorial Algorithms: Theory and Practice , 1977 .

[111]  J. Biggins.  The first- and last-birth problems for a multitype age-dependent branching process , 1976, Advances in Applied Probability.

[112]  J. Biggins.  Asymptotic properties of the branching random walk , 1976 .

[113]  Derick Wood,et al.  Locally Balanced Binary Trees , 1976, Comput. J..

[114]  D. P. Kennedy,et al.  The Galton-Watson process conditioned on the total progeny , 1975, Journal of Applied Probability.

[115]  V. V. Petrov,et al.  Sums of Independent Random Variables , 1976 .

[116]  J. Kingman.  The First Birth Problem for an Age-dependent Branching Process , 1975 .

[117]  P. Holgate,et al.  Branching Processes with Biological Applications , 1977 .

[118]  J. Hammersley.  Postulates for Subadditive Processes , 1974 .

[119]  J. Kingman.  Subadditive Ergodic Theory , 1973 .

[120]  J. Moon.  Random walks on random trees , 1973, Journal of the Australian Mathematical Society.

[121]  de Ng Dick Bruijn,et al.  THE AVERAGE HEIGHT OF PLANTED PLANE TREES , 1972 .

[122]  Ronald C. Read,et al.  Graph theory and computing , 1972 .

[123]  B. M. Brown,et al.  An invariance principle and some convergence rate results for branching processes , 1971 .

[124]  C. C. Heyde,et al.  Some central limit analogues for supercritical Galton-Watson processes , 1971, Journal of Applied Probability.

[125]  S. Nagaev,et al.  Probability inequalities for sums of independent random variables with values in a Banach space , 1971 .

[126]  A. Pakes,et al.  Some limit theorems for the total progeny of a branching process , 1971, Advances in Applied Probability.

[127]  D. Darling.  The Galton-Watson process with infinite mean , 1970, Journal of Applied Probability.

[128]  C. Heyde.  A rate of convergence result for the super-critical Galton-Watson process , 1970, Journal of Applied Probability.

[129]  Edward G. Coffman,et al.  File structures using hashing functions , 1970, CACM.

[130]  A. Meir,et al.  The distance between points in random trees , 1970 .

[131]  J. Moon.  Counting labelled trees , 1970 .

[132]  M. Dwass.  The total progeny in a branching process and a related random walk , 1969, Journal of Applied Probability.

[133]  S. Dharmadhikari,et al.  BOUNDS ON MOMENTS OF CERTAIN RANDOM VARIABLES , 1969 .

[134]  E. Seneta.  Functional equations and the Galton-Watson process , 1969, Advances in Applied Probability.

[135]  V. E. Stepanov.  On the Distribution of the Number of Vertices in Strata of a Random Tree , 1969 .

[136]  Charles J. Mode,et al.  A general age-dependent branching process. II , 1968 .

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

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

[139]  Eugene Seneta,et al.  A Refinement of Two Theorems in the Theory of Branching Processes , 1967 .

[140]  H. Kesten,et al.  A Limit Theorem for Multidimensional Galton-Watson Processes , 1966 .

[141]  Frank Spitzer,et al.  The Galton-Watson Process with Mean One and Finite Variance , 1966 .

[142]  D. Kendall.  Branching Processes Since 1873 , 1966 .

[143]  William C. Lynch,et al.  More Combinatorial Properties of Certain Trees , 1965, Comput. J..

[144]  Robert S. Shankland,et al.  Handbook of Mathematical Tables , 1963 .

[145]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[146]  R. R. Bahadur,et al.  On Deviations of the Sample Mean , 1960 .

[147]  John Riordan,et al.  The Enumeration of Trees by Height and Diameter , 1960, IBM J. Res. Dev..

[148]  Edward Fredkin,et al.  Trie memory , 1960, Commun. ACM.

[149]  M. Okamoto.  Some inequalities relating to the partial sum of binomial probabilities , 1959 .

[150]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[151]  Richard Bellman,et al.  ON AGE-DEPENDENT BINARY BRANCHING PROCESSES' , 1952 .

[152]  W. Feller.  An Introduction to Probability Theory and Its Applications , 1959 .

[153]  R. Eric O'Connor.  Canadian Mathematical Congress , 1945 .

[154]  J. Marcinkiewicz.  Sur les fonctions indépendantes , 1938 .

[155]  Arthur Cayley,et al.  The Collected Mathematical Papers: On the analytical forms called trees , 1881 .