Approximating functions by their Poisson transform
Information Processing Letters
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Automatic average-case analysis of algorithms
Theoretical Computer Science - Theme issue on the algebraic and computing treatment of noncommutative power series
Some observations on skip-lists
Information Processing Letters
Skip lists and probabilistic analysis of algorithms
Skip lists and probabilistic analysis of algorithms
The path length of random skip lists
Acta Informatica
Mellin transforms and asymptotics: harmonic sums
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Mellin transforms and asymptotics: finite differences and Rice's integrals
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Combinatorics of geometrically distributed random variables: left-to-right maxima
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The Binomial Transform and its Application to the Analysis of Skip Lists
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
| Hi-index | 5.23 |
To any sequence of real numbers 〈an〉 n ≥ 0, we can associate another sequence 〈âs〉s ≥ 0 which Knuth calls its binomial transform. This transform is defined through the rule âs = Bsan=Σn(-1)n(s n) an.We study the properties of this transform, obtaining rules for its manipulation and a table of transforms, that allow us to invert many transforms by inspection.We use these methods to perform a detailed analysis of skip lists, a probabilistic data structure introduced by Pugh as an alternative to balanced trees. In particular, we obtain the mean and variance for the cost of searching for the first or the last element in the list (confirming results obtained previously by other methods), and also for the cost of searching for a random element (whose variance was not known).We obtain exact solutions, although not always in closed form. From them we are able to find the corresponding asymptotic expressions.