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.WORST-CASE ADAPTIVE (INTERNAL) SORTING ALGORITHMS 1.1 Generic Sort 1.2 Cook--Kim division 1.3 Partition Sort 1.4 Exponential Search 1.5 Adaptive Merging 2.EXPECTED-CASE ADAPTIV

Indexing of high-dimensional 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 high-dimensional index structure based on peer-to-peer 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 load-balancing 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

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 worst-case 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...

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 ...

We consider a serialized coin-tossing 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.