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 peer-to-peer 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, simple and straightforward algorithms can be used to construct a skip graph, insert new nodes into it, search it, and detect and repair errors in a skip graph introduced due to node failures.

Abstract. For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q–analogues for these parameters from the usual permutation model are obtained. 1.

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 average--case analysis of algorithms. It reviews the use of Mellin-Perron formulae and of Mellin transforms in this context. Applications include: divide-and-conquer recurrences, maxima finding, mergesort, digital trees and plane trees.

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, for fixed r and n !1. 1.

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

doi:10.2298/AADM0802234P