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Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2196 (36 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Randomized Algorithms
, 1994
"... We have already seen some uses of randomization in the design of online algorithms. In these notes, we shall describe other important illustrations of randomized algorithms in other areas of the theory of algorithms. For those interested in learning more about randomized algorithms, we strongly rec ..."
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We have already seen some uses of randomization in the design of online algorithms. In these notes, we shall describe other important illustrations of randomized algorithms in other areas of the theory of algorithms. For those interested in learning more about randomized algorithms, we strongly
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 532 (5 self)
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distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical
Inducing Features of Random Fields
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the ..."
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Cited by 670 (10 self)
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the KullbackLeibler divergence between the model and the empirical distribution of the training data. A greedy algorithm determines how features are incrementally added to the field and an iterative scaling algorithm is used to estimate the optimal values of the weights. The random field models and techniques
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental
Data Streams: Algorithms and Applications
, 2005
"... In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerg ..."
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Cited by 533 (22 self)
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emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudorandom computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic
Randomized Algorithms
"... I warrant that the content of this dissertation is the direct result of my own work and that any use made in it of published or unpublished material is fully and correctly referenced. Signed: Date: ..."
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I warrant that the content of this dissertation is the direct result of my own work and that any use made in it of published or unpublished material is fully and correctly referenced. Signed: Date:
Randomized Algorithms
, 1999
"... (uv); without loss of generality assume that (uv) 2 S. This defines the cut ((S \Gamma (uv)) [ fug [ fvg; S) 2 G.) ffl The values of these cuts are equal. (Any edges of the form (xy) which cross the cut (S; S) where x; y = 2 fu; vg remain in the corresponding cut of G. Those edges of the form ((uv ..."
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(uv); without loss of generality assume that (uv) 2 S. This defines the cut ((S \Gamma (uv)) [ fug [ fvg; S) 2 G.) ffl The values of these cuts are equal. (Any edges of the form (xy) which cross the cut (S; S) where x; y = 2 fu; vg remain in the corresponding cut of G. Those edges of the form ((uv)y), by definition, have weight equal to the sum of at least one of the edges (uy) and/or (vy) which cross the corresponding cut of G.) ffl Contractions commute. It immediately follows that the value of the mincut of G=(uv) is at least as great as the value of the mincut of G. 1 We now pr
Results 1  10
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