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Hierarchical Agglomerative Graph Clustering in Poly-Logarithmic Depth [article]

Laxman Dhulipala and David Eisenstat and Jakub Łącki and Vahab Mirronki and Jessica Shi
2022 arXiv   pre-print
In particular, we provide a (1+ϵ)-approximation algorithm for this problem on m edge graphs using Õ(m) work and poly-logarithmic depth.  ...  We also show that ParHAC can cluster one of the largest publicly available graph datasets with 124 billion edges in a little over three hours using a commodity multicore machine.  ...  Specifically, in the i-th round, the SCC algorithm runs a round of Affinity on the graph induced by all edges with weight at least T i where T i is the weight threshold on the i-th round.  ... 
arXiv:2206.11654v1 fatcat:l3qpzk2grfh6tcqrjzoraufeqi

Parallel and Scalable Heat Methods for Geodesic Distance Computation [article]

Jiong Tao, Juyong Zhang, Bailin Deng, Zheng Fang, Yue Peng, Ying He
2019 arXiv   pre-print
Moreover, we employ a similar breadth-first strategy to derive a parallel Gauss-Seidel solver for the diffusion step in the heat method.  ...  In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes.  ...  Therefore, for a mesh with no boundary, the face-based formulation requires at least a storage space of (6N F + 15N E ) · M bytes, where M is the width of a floating point value.  ... 
arXiv:1812.06060v3 fatcat:ozaxu5w2u5b3lfmcbr5jl2gjzq

Minor Sparsifiers and the Distributed Laplacian Paradigm [article]

Sebastian Forster and Gramoz Goranci and Yang P. Liu and Richard Peng and Xiaorui Sun and Mingquan Ye
2022 arXiv   pre-print
For the mincost flow and the negative weight shortest path problems, our results constitute the first exact distributed algorithms running in a sublinear number of rounds.  ...  optimization problems on graphs via a series of Laplacian systems.  ...  This notion of rooting can be made more explicit: we can compute directions for all edges in the spanning tree → ( ) that point to the corresponding root vertex → ( ).  ... 
arXiv:2012.15675v3 fatcat:bvoh5dhsirehpcx46vl54xokya

Ultrasparse Ultrasparsifiers and Faster Laplacian System Solvers [article]

Arun Jambulapati, Aaron Sidford
2020 arXiv   pre-print
In this paper we provide an O(m (loglog n)^O(1)log(1/ϵ))-expected time algorithm for solving Laplacian systems on n-node m-edge graphs, improving improving upon the previous best expected runtime of O(  ...  of relative condition number at most k^2.  ...  Aaron Sidford was support in part by a Microsoft Research Faculty Fellowship, NSF CAREER Award CCF-1844855, NSF Grant CCF-1955039, a PayPal research gift award, and a Sloan Research Fellowship.  ... 
arXiv:2011.08806v1 fatcat:xswiqovfgjc3ddrgmpfq6npdpa

TMVA - Toolkit for Multivariate Data Analysis [article]

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski (+14 others)
2009 arXiv   pre-print
With version 4, TMVA has been extended to multivariate regression of a real-valued target vector. Regression is invoked through the same user interfaces as classification.  ...  Integrated into the analysis framework ROOT, TMVA is a toolkit which hosts a large variety of multivariate classification algorithms.  ...  The type is used to inform the method whether a variable takes continuous floating point or discrete values. 4 Note that 'F' indicates any floating point type, i.e., float and double.  ... 
arXiv:physics/0703039v5 fatcat:xec4mqsl5rgsrnljp2z2n6brj4

Covariance Propagation and Next Best View Planning for 3D Reconstruction [chapter]

Sebastian Haner, Anders Heyden
2012 Lecture Notes in Computer Science  
In particular, the problem of view planning is considered, and continuous and discrete optimization-based algorithms are given for how to plan the path of a sensor to its destination, while balancing the  ...  Finally, a practical method for calibrating a set of cameras under refraction is given, including an algorithm for efficient refractive bundle adjustment. e content of the thesis is based on the following  ...  We now have L(θ) ∝ ∼ R 2N e − x−x 2 R · e − f (X,θ)−x 2 JQJ dx, (6. − log L(θ) ∝ ∼ x − f (X, θ) 2 R+JQJ , (6.10) which can be solved using an iteratively reweighted nonlinear least-squares algorithm.  ... 
doi:10.1007/978-3-642-33709-3_39 fatcat:vdnwuw3e65ds7m7l76oatcycuq

Design of large polyphase filters in the Quadratic Residue Number System

Gian Carlo Cardarilli, Alberto Nannarelli, Yann Oster, Massimo Petricca, Marco Re
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
Iteratively Reweighted Least Squares approximation used to find the inverse solution of an underdetermined linear system when the source vector is assumed to be sparse.  ...  In this paper, a redundant decimal floating-point adder is proposed with the ultimate objective of enhancing the speed of the decimal floating-point addition.  ... 
doi:10.1109/acssc.2010.5757589 fatcat:ccxnu5owr5fyrcjcqukumerueq

Design of LDPC decoders for improved low error rate performance: quantization and algorithm choices

Zhengya Zhang, Lara Dolecek, Borivoje Nikolic, Venkat Anantharam, Martin Wainwright
2009 IEEE Transactions on Communications  
a factor (check) node (shown as a square).  ...  limit when decoded iteratively using a message-passing algorithm [29, 45, 46, 57] .  ... 
doi:10.1109/tcomm.2009.11.080105 fatcat:nokjs4c6rbddnp6nijzkmuhulu

Bundle Adjustment — A Modern Synthesis [chapter]

Bill Triggs, Philip F. McLauchlan, Richard I. Hartley, Andrew W. Fitzgibbon
2000 Lecture Notes in Computer Science  
The theory is developed for general robust cost functions rather than restricting attention to traditional nonlinear least squares.  ...  Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates.  ...  In fact, the normal equations are just one of many methods of solving the weighted linear least squares problem 5 min δx 1 2 (J δx − z) W (J δx − z) .  ... 
doi:10.1007/3-540-44480-7_21 fatcat:jm2ewshh5bejhnv5dixghvp6y4

A Machine Learning Approach to Recovery of Scene Geometry from Images [article]

Hoang Trinh
2010 arXiv   pre-print
We demonstrate the use of our unsupervised CRF learning algorithm for a parameterized slanted-plane stereo vision model involving shape from texture cues.  ...  We employ a slanted-plane stereo vision model in which we use a fixed over-segmentation to segment the left image into coherent regions called superpixels, then assign a disparity plane for each superpixel  ...  BP, graph cuts or tree-reweighted message passing.  ... 
arXiv:1007.2958v1 fatcat:p37agro3drgbhnidt2hx3tykbq

LHAPDF6: parton density access in the LHC precision era

Andy Buckley, James Ferrando, Stephen Lloyd, Karl Nordström, Ben Page, Martin Rüfenacht, Marek Schönherr, Graeme Watt
2015 European Physical Journal C: Particles and Fields  
In this paper we present the LHAPDF 6 library, a ground-up re-engineering of the PDFLIB/LHAPDF paradigm for PDF access which removes all limits on use of concurrent PDF sets, massively reduces static memory  ...  The new design, restricted for now to interpolated PDFs, uses centralised numerical routines and a powerful cascading metadata system to decouple software releases from provision of new PDF data and allow  ...  and a fast numeric ASCII parser code.  ... 
doi:10.1140/epjc/s10052-015-3318-8 fatcat:jbjbuk74lnb2pfg5sgixdvw5tm

Hyperbox based machine learning algorithms: A comprehensive survey [article]

Thanh Tung Khuat, Dymitr Ruta, Bogdan Gabrys
2019 arXiv   pre-print
Learning algorithms using hyperboxes as fundamental representational and building blocks are a branch of machine learning methods.  ...  Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new information and knowledge from different data sources.  ...  An open hyperbox isa hyperbox with at least one dimension undefined by its minimum and maximum points, whereas a closed hyperbox is the one with all its minimum and maximum vertices defined.  ... 
arXiv:1901.11303v3 fatcat:ak66d74lxvbp7j3hjg4mzvqlr4

Measurement of beauty production in deep inelastic scattering at HERA

S. Chekanov, M. Derrick, J.H. Loizides, S. Magill, S. Miglioranzi, B. Musgrave, J. Repond, R. Yoshida, M.C.K. Mattingly, N. Pavel, P. Antonioli, G. Bari (+322 others)
2004 Physics Letters B  
The beauty production cross section for deep inelastic scattering events with at least one hard jet in the Breit frame together with a muon has been measured, for photon virtualities Q^2 > 2 GeV^2, with  ...  the ZEUS detector at HERA using integrated luminosity of 72 pb^-1.  ...  Therefore only a loose cut of at least three muon layers is possible.  ... 
doi:10.1016/j.physletb.2004.08.048 fatcat:ivpdfg3sprafnhthizim2dojly

The Algorithmic Foundations of Differential Privacy

Cynthia Dwork, Aaron Roth
2013 Foundations and Trends® in Theoretical Computer Science  
This book was used in a course taught by Salil Vadhan and Jon Ullman, whose students also provided careful feedback.  ...  This book has also benefited from conversations with many other colleagues, including Moritz Hardt, Ilya Mironov, Sasho Nikolov, Kobbi Nissim, Mallesh Pai, Benjamin Pierce, Adam Smith, Abhradeep Thakurta  ...  of L ∞ norm Ω(min{k/ε, d/ε}) with probability at least 1/2 on some databases of weight at most n.  ... 
doi:10.1561/0400000042 fatcat:jk3mb6ltcfeqzeyvpyznpohuja

Linear Programming: Foundations and Extensions

R J Vanderbei
1998 Journal of the Operational Research Society  
(j) How does this primal-dual affine-scaling algorithm compare with the iteratively reweighted least squares algorithm defined in Section 12.5?  ...  Iteratively Reweighted Least Squares Even though calculus cannot be used to obtain an explicit formula for the solution to the L 1 -regression problem, it can be used to obtain an iterative procedure that  ...  Complexity of the Predictor-Corrector Algorithm. Of course, in practice we don't run an infinite number of iterations. Instead, we set a priori a threshold and stop when µ (k) falls below it.  ... 
doi:10.1038/sj.jors.2600987 fatcat:d4xmw4dy7rflnextmoz2bytkqa
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