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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 235 (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
A Survey of Adaptive Sorting Algorithms
, 1992
"... Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems  Sorting and Searching; E.5 [Data]: Files  Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics  Probabilistic algorithms; E.2 [Data Storage Represe ..."
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Cited by 65 (3 self)
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Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems  Sorting and Searching; E.5 [Data]: Files  Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics  Probabilistic algorithms; E.2 [Data Storage Representation]: Composite structures, linked representations. General Terms: Algorithms, Theory. Additional Key Words and Phrases: Adaptive sorting algorithms, Comparison trees, Measures of disorder, Nearly sorted sequences, Randomized algorithms. A Survey of Adaptive Sorting Algorithms 2 CONTENTS INTRODUCTION I.1 Optimal adaptivity I.2 Measures of disorder I.3 Organization of the paper 1.WORSTCASE ADAPTIVE (INTERNAL) SORTING ALGORITHMS 1.1 Generic Sort 1.2 CookKim division 1.3 Partition Sort 1.4 Exponential Search 1.5 Adaptive Merging 2.EXPECTEDCASE ADAPTIV
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 19 (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
Parallel Update And Search In Skip Lists
"... We present a PRAM implementation of a parallel dictionary with skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to explain and implement. All of them are iterative. They can be ..."
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Cited by 1 (0 self)
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We present a PRAM implementation of a parallel dictionary with skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to explain and implement. All of them are iterative. They can be implemented in the EREW PRAM model using O(k) processors in expected time O(log n + log k). The probability that there is a significant deviation from the expected time decreases as O(n \Gamma2 ). 1 INTRODUCTION A skip list is a randomized data structure that can be used for representing abstract data types such as dictionaries and ordered lists. Skip lists were introduced by W. Pugh in 1990 11 and are an alternative to balanced trees; although they have bad worstcase performance, the randomization process involved in their construction guarantees an expected sequential performance of the same order of magnitude as that of balanced trees. Moreover, the probability of the search time o...
A TopDown Design of a Parallel Dictionary using Skip Lists
, 1994
"... We present a top down design of a parallel PRAM dictionary using skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to implement on real machines. All of them are iterative. Th ..."
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Cited by 1 (0 self)
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We present a top down design of a parallel PRAM dictionary using skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to implement on real machines. All of them are iterative. They can be implemented in the EREW PRAM model using O(k) processors in expected time O(log n+ log k). The probability that there is a significant deviation from the expected time decreases as O(n \Gamma2 ) in the search and as O(n \Gamma2 + k \Gamma2 ) in the insertion and deletion. 1 Introduction Parallel dictionaries are important data structures widely studied. In a systolic framework, priority queues and search trees were designed by C.E. Leiserson in [13]. Later, M.J. Atallah and S.R. Kosaraju [1] developped a generalized dictionary where a sequence of operations can be pipelined at constant rate. In the PRAM context, W. Paul, U. Vishkin and H. Wagener developed and analyzed ...
Applied Probability Trust (1 February 2011) ASYMPTOTIC PROPERTIES OF A LEADER ELECTION ALGO RITHM
"... We consider a serialized cointossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically it turns o ..."
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We consider a serialized cointossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically it turns out to be a geometric distribution. Rice’s method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable. Keywords: Leader election, analytic combinatorics, Rice’s method, fixed point, contraction method, Wasserstein metric space, weak convergence.