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Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 738 (18 self)
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in the problem graph: ( 1) O(n log n + m) for the singlesource shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the allpairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite
Surface Simplification Using Quadric Error Metrics
"... Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplifi ..."
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Cited by 1174 (16 self)
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simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm
A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 869 (3 self)
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A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2725 (61 self)
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variation denoising, and multiscale edge denoising. Basis Pursuit in highly overcomplete dictionaries leads to largescale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 768 (3 self)
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random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (33 self)
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All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 429 (21 self)
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This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle
Robust Distributed Network Localization with Noisy Range Measurements
, 2004
"... This paper describes a distributed, lineartime algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherw ..."
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Cited by 400 (20 self)
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that otherwise corrupt localization computations. We formulate the localization problem as a twodimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable
A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics
 In Proceedings of the 35th Annual ACM Symposium on Theory of Computing
, 2003
"... In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; t ..."
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Cited by 305 (8 self)
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In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight
Improved Decoding of ReedSolomon and AlgebraicGeometry Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes ..."
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Cited by 345 (44 self)
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Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding Reed
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