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Skip Graphs
 Proc. of the 14th Annual ACMSIAM Symp. on Discrete Algorithms
, 2003
"... Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peertopeer systems, and by providin ..."
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Cited by 306 (9 self)
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Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peertopeer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, constructing, inserting new nodes into, searching a skip graph, and detecting and repairing errors in the data structure introduced by node failures can be done using simple and straightforward algorithms. 1
Mellin Transforms And Asymptotics: Harmonic Sums
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative of the i ..."
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Cited by 202 (12 self)
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This survey presents a unified and essentially selfcontained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the averagecase analysis of algorithms. It relies on the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. The method applies to harmonic sums that are superpositions of rather arbitrary "harmonics" of a common base function. Its principle is a precise correspondence between individual terms in the asymptotic expansion of an original function and singularities of the transformed function. The main applications are in the area of digital data structures, probabilistic algorithms, and communication theory.
COMBINATORICS OF GEOMETRICALLY DISTRIBUTED RANDOM VARIABLES: VALUE AND POSITION OF LARGE LEFT–TO–RIGHT MAXIMA
, 2008
"... For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth left–to–right maximum counted from the right, for fixed r and n → ∞. This complements previous research [5] where the analogous questions were considered fo ..."
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Cited by 42 (13 self)
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For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth left–to–right maximum counted from the right, for fixed r and n → ∞. This complements previous research [5] where the analogous questions were considered for the rth left–to–right maximum counted from the left.
Normal Approximations of the Number of Records in Geometrically Distributed Random Variables
 Alg
, 1998
"... We establish the asymptotic normality of the number of upper records in a sequence of iid geometric random variables. Large deviations and local limit theorems as well as approximation theorems for the number of lower records are also derived. 1 ..."
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Cited by 15 (1 self)
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We establish the asymptotic normality of the number of upper records in a sequence of iid geometric random variables. Large deviations and local limit theorems as well as approximation theorems for the number of lower records are also derived. 1
Combinatorics of Geometrically Distributed Random Variables: Value and Position of the rth LefttoRight Maximum
 DISCRETE MATH
, 1999
"... For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1 ..."
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Cited by 10 (6 self)
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For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the rth lefttoright maximum, for fixed r and n !1. 1
The Average Case Analysis of Algorithms: Mellin Transform Asymptotics
, 1996
"... This report is part of a series whose aim is to present in a synthetic way the major methods of "analytic combinatorics" needed in the averagecase analysis of algorithms. It reviews the use of MellinPerron formulae and of Mellin transforms in this context. Applications include: dividea ..."
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Cited by 9 (0 self)
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This report is part of a series whose aim is to present in a synthetic way the major methods of "analytic combinatorics" needed in the averagecase analysis of algorithms. It reviews the use of MellinPerron formulae and of Mellin transforms in this context. Applications include: divideandconquer recurrences, maxima finding, mergesort, digital trees and plane trees.
Records in geometrically distributed words: sum of positions
 Applicable Analysis and Discrete Mathematics
, 1994
"... Abstract. Kortchemski introduced a new parameter for random permutations: the sum of the positions of the records. We investigate this parameter in the context of random words, where the letters are obtained by geometric probabilities. We find a relation for a bivariate generating function, from wh ..."
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Cited by 4 (0 self)
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Abstract. Kortchemski introduced a new parameter for random permutations: the sum of the positions of the records. We investigate this parameter in the context of random words, where the letters are obtained by geometric probabilities. We find a relation for a bivariate generating function, from which we can obtain the expectation, exactly and asymptotically. In principle, one could get all moments from it, but the computations would be huge.
drecords in geometrically distributed random variables
 DISCRETE MATHEMATICS & THEORETICAL COMPUTER SCIENCE
, 2006
"... We study d–records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d–record occurs, when one computes the d–largest values, and the variable maintaining it changes its value while the seq ..."
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Cited by 3 (0 self)
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We study d–records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d–record occurs, when one computes the d–largest values, and the variable maintaining it changes its value while the sequence is scanned from left to right. This is done for the “strict model,” but a “weak model ” is also briefly investigated. We also discuss the limit q → 1 (q the parameter of the geometric distribution), which leads to the model of random permutations.
Analysis of a new skip list variant
, 2006
"... For a skip list variant, introduced by Cho and Sahni, we analyse what is the analogue of horizontal plus vertical search cost in the original skip list model. While the average in Pugh’s original version behaves likeÉÐÓ�ÉÒ, withÉ�Õa parameter, it is here given byÉ ÐÓ�ÉÒ. ..."
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For a skip list variant, introduced by Cho and Sahni, we analyse what is the analogue of horizontal plus vertical search cost in the original skip list model. While the average in Pugh’s original version behaves likeÉÐÓ�ÉÒ, withÉ�Õa parameter, it is here given byÉ ÐÓ�ÉÒ.