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27
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
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.
Randomized Binary Search Trees
 Journal of the ACM
, 1997
"... In this paper we present randomized algorithms over binary search trees such that: a) the insertion of a set of keys, in any fixed order, into an initially empty tree always produces a random binary search tree; b) the deletion of any key from a random binary search tree results in a random binary s ..."
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Cited by 28 (2 self)
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In this paper we present randomized algorithms over binary search trees such that: a) the insertion of a set of keys, in any fixed order, into an initially empty tree always produces a random binary search tree; b) the deletion of any key from a random binary search tree results in a random binary search tree; c) the random choices made by the algorithms are based upon the sizes of the subtrees of the tree; this implies that we can support accesses by rank without additional storage requirements or modification of the data structures; and d) the cost of any elementary operation, measured as the number of visited nodes, is the same as the expected cost of its standard deterministic counterpart; hence, all search and update operations have guaranteed expected cost O(log n), but now irrespective of any assumption on the input distribution. 1. Introduction Given a binary search tree (BST, for short), common operations are the search of an item given its key and the retrieval of the inform...
Skipindex: Towards a scalable peertopeer index service for high dimensional data
 Princeton Univ
, 2004
"... Indexing of highdimensional data is essential for building applications such as multimedia retrieval, data mining, and spatial databases. Traditional index structures rely on centralized processing. This approach does not scale with the rapidly increasing amount of application data available on mas ..."
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Cited by 22 (1 self)
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Indexing of highdimensional data is essential for building applications such as multimedia retrieval, data mining, and spatial databases. Traditional index structures rely on centralized processing. This approach does not scale with the rapidly increasing amount of application data available on massively distributed systems like the Internet. In this paper, we propose a distributed highdimensional index structure based on peertopeer overlay routing. A new routing scheme is used to lookup data keys in the distributed index, which guarantees logarithmic lookup and maintenance cost, even in the face of skewed datasets. We propose a novel nearest neighbor (NN) query scheme that can substantially reduce search cost by sacrificing a small amount of precision. We propose a loadbalancing mechanism that partitions the high dimensional search space in a balanced manner. We then analyze the performance of our proposed using a variety of metrics with simulation as well as a functional PlanetLab implementation. 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 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
Analysis of an Optimized Search Algorithm for Skip Lists
 Theoretical Computer Science
, 1994
"... It was suggested in [8] to avoid redundant queries in the skip list search algorithm by marking those elements whose key has already been checked by the search algorithm. We present here a precise analysis of the total search cost (expectation and variance), where the cost of the search is measured ..."
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Cited by 13 (5 self)
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It was suggested in [8] to avoid redundant queries in the skip list search algorithm by marking those elements whose key has already been checked by the search algorithm. We present here a precise analysis of the total search cost (expectation and variance), where the cost of the search is measured in terms of the number of keyto key comparison.These results are then compared with the corresponding values of the standard search algorithm. 1 Introduction Skip lists have recently been introduced as a type of listbased data structure that may substitute search trees [9]. A set of n elements is stored in a collection of sorted linear linked lists in the following manner: all elements are stored in increasing order in a linked list called level 1 and, recursively, each element which appears in the linked list level i is included with independent probability q (0 ! q ! 1) in the linked list level i + 1. The level of an element x is the number of linked lists it belongs to. For each elemen...
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
On the Cost of Persistence and Authentication in Skip Lists
"... We present an extensive experimental study of authenticated data structures for dictionaries and maps implemented with skip lists. We consider realizations of these data structures that allow us to study the performance overhead of authentication and persistence. We explore various design decisions ..."
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Cited by 10 (8 self)
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We present an extensive experimental study of authenticated data structures for dictionaries and maps implemented with skip lists. We consider realizations of these data structures that allow us to study the performance overhead of authentication and persistence. We explore various design decisions and analyze the impact of garbage collection and virtual memory paging, as well. Our empirical study confirms the efficiency of authenticated skip lists and offers guidelines for incorporating them in various applications.
A Note on Alternating Sums
 Electron. J. Combin
, 1995
"... We present some results on a certain type of alternating sums which frequently arise in connection with the averagecase analysis of algorithms and data structures. Whereas the socalled Rice's method for treating such sums uses complex contour integration we perform manipulations of generating ..."
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Cited by 9 (0 self)
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We present some results on a certain type of alternating sums which frequently arise in connection with the averagecase analysis of algorithms and data structures. Whereas the socalled Rice's method for treating such sums uses complex contour integration we perform manipulations of generating functions in order to get explicit results from which asymptotic estimates follow immediately. 1 Introduction In the present paper we deal with alternating sums of the type N X k=a / N k ! (\Gamma1) k f(k); (1) where a is a natural number fulfilling 0 a N . If a = 0; this expression is an Nth order difference of the sequence (f(n)). Sums of the referred type occur frequently in the average case analysis of divideandconquer algorithms resp. data structures like tries or digital search trees. We refer to [2], [7], [9], [10] and [13] for a number of examples. A standard method for the treatment of sums of that type, attributed to S.O.Rice by D.E.Knuth [7], but in fact already contain...
The first descent in samples of geometric random variables and permutations
"... For words of length n, generated by independent geometric random variables, we study the average initial and end heights of the first strict and weak descents in the word. Higher moments and limiting distributions are also derived. In addition we compute the average initial and end height of the fir ..."
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Cited by 5 (3 self)
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For words of length n, generated by independent geometric random variables, we study the average initial and end heights of the first strict and weak descents in the word. Higher moments and limiting distributions are also derived. In addition we compute the average initial and end height of the first descent for a random permutation of n letters.