The analysis of hybrid trie structures

This paper provides a detailed analysis of various implementations of digital tries, including the «ternary search tries» of Bentley and Sedgewick. The methods employed combine symbolic uses of generating functions, Poisson models, and Mellin transforms. Theoretical results are matched against real-life data and justify the claim that ternary search tries are a highly efficient dynamic dictionary structure for strings and textual data.

[1]  Robert Sedgewick,et al.  Fast algorithms for sorting and searching strings , 1997, SODA '97.

[2]  G. H. Gonnet,et al.  Handbook of algorithms and data structures: in Pascal and C (2nd ed.) , 1991 .

[3]  Philippe Jacquet,et al.  Analysis of digital tries with Markovian dependency , 1991, IEEE Trans. Inf. Theory.

[4]  Luis Trabb Pardo.  Set representation and set intersection , 1978 .

[5]  Philippe Flajolet,et al.  Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search , 1992, Discret. Appl. Math..

[6]  Harry A. Clampett.  Randomized binary searching with tree structures , 1964, CACM.

[7]  William H. Burge.  An Analysis of Binary Search Trees Formed from Sequences of Nondistinct Keys , 1976, JACM.

[8]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[9]  Philippe Flajolet,et al.  Mellin Transforms and Asymptotics: Harmonic Sums , 1995, Theor. Comput. Sci..

[10]  Dominic J. A. Welsh,et al.  Codes and cryptography , 1988 .

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

[12]  Ronald L. Rivest,et al.  Partial-Match Retrieval Algorithms , 1976, SIAM J. Comput..

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

[14]  Philippe Flajolet,et al.  An introduction to the analysis of algorithms , 1995 .

[15]  Philippe Flajolet,et al.  Partial match retrieval of multidimensional data , 1986, JACM.

[16]  Donald E. Knuth,et al.  The art of computer programming: sorting and searching (volume 3) , 1973 .

[17]  J. Ian Munro,et al.  Self-organizing binary search trees , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[18]  Philippe Flajolet,et al.  Continued Fraction Algorithms, Functional Operators, and Structure Constants , 1998, Theor. Comput. Sci..

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