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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 ..."
Abstract

Cited by 248 (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
Combinatorics of geometrically distributed random variables: new qtangent and qsecant numbers
 Int. J. Math. Math. Sci
"... ..."
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 12 (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.
Combinatorics of Geometrically Distributed Random Variables: Value and Position of the rth LefttoRight Maximum
 Discrete Math
"... 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 8 (5 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.
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 7 (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
Abstract Theoretical Computer Science Mellin transforms and asymptotics: Harmonic sums
"... for their pioneering works on Mellin transforms and combinatorics 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 algori ..."
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for their pioneering works on Mellin transforms and combinatorics 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.
Analysis of a new skip list variant
"... 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. Keywords: Skip list, Rice’s ..."
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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. Keywords: Skip list, Rice’s method, moments, functional equation, asymptotic expansion. 1