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Optimal Adaptive Algorithms for Finding the Nearest and Farthest Point on a Parametric Black-Box Curve [article]

Ilya Baran, Erik D. Demaine
2004 arXiv   pre-print
In this model, we consider the nearest-point-on-curve and farthest-point-on-curve problems: given a curve C and a point p, find a point on C nearest to p or farthest from p.  ...  We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space.  ...  In this paper, we solve two of the most basic proximity queries about black-box Lipschitz curves: given a curve C and a point p, find a point on C that is closest to p (nearest point), and find a point  ... 
arXiv:cs/0307005v3 fatcat:gt562grc3fhmbfnz26pt7ve7ku

Optimal adaptive algorithms for finding the nearest and farthest point on a parametric black-box curve

Ilya Baran, Erik D. Demaine
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04  
In this model, we consider the nearest-point-on-curve and farthest-point-on-curve  ...  We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space.  ...  In this paper, we solve two of the most basic proximity queries about black-box Lipschitz curves: given a curve C and a point p, find a point on C that is closest to p (nearest point), and find a point  ... 
doi:10.1145/997817.997852 dblp:conf/compgeom/BaranD04 fatcat:h5edzoxwtnhulbir47tpf3q6ma

OPTIMAL ADAPTIVE ALGORITHMS FOR FINDING THE NEAREST AND FARTHEST POINT ON A PARAMETRIC BLACK-BOX CURVE

ILYA BARAN, ERIK D. DEMAINE
2005 International journal of computational geometry and applications  
In this model, we consider the nearest-point-on-curve and farthest-point-on-curve  ...  We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space.  ...  In this paper, we solve two of the most basic proximity queries about black-box Lipschitz curves: given a curve C and a point p, find a point on C that is closest to p (nearest point), and find a point  ... 
doi:10.1142/s0218195905001737 fatcat:koe5rcmknzbi7nkvu4yv3tyi6m

ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions

William B. March, Bo Xiao, George Biros
2015 SIAM Journal on Scientific Computing  
As a highlight, we report results for Gaussian kernel sums for 100 million points in 64 dimensions, for one million points in 1000 dimensions, and for problems in which the Gaussian kernel has a variable  ...  Pruning is not done using bounding boxes but rather combinatorially using a sparsified nearest-neighbor graph of the input distribution.  ...  (For example, the intrinsic dimension of points sampled on a 3D curve is one.)  ... 
doi:10.1137/140989546 fatcat:nh5uoa5djrfabfuoif25adzc4y

ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions [article]

William B. March, Bo Xiao, George Biros
2015 arXiv   pre-print
We report results for Gaussian kernel sums for 100 million points in 64 dimensions, for one million points in 1000 dimensions, and for problems in which the Gaussian kernel has a variable bandwidth.  ...  Pruning is not done using bounding boxes but rather combinatorially using a sparsified nearest-neighbor graph of the input.  ...  (For example, the intrinsic dimension of points sampled on a 3D curve is one.)  ... 
arXiv:1410.0260v3 fatcat:zmcyqcqvargllbz4dvjglv2pba

iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes [article]

Eliodoro Chiavazzo, Ronald R. Coifman, Roberto Covino, C. William Gear, Anastasia S. Georgiou, Gerhard Hummer, Ioannis G. Kevrekidis
2016 arXiv   pre-print
We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extraction of coarse-grained  ...  The added value comes from biasing the simulator towards new, unexplored phase space regions by exploiting the smoothness of the (gradually, as the exploration progresses) revealed intrinsic low-dimensional  ...  Acknowledgments This work was partially supported by the US National Science Foundation, the US AFOSR (Dr.  ... 
arXiv:1701.01513v1 fatcat:qxd6jihhgjdwdnm7ct7s6pssja

Semialgebraic Range Reporting and Emptiness Searching with Applications

Micha Sharir, Hayim Shaul
2011 SIAM journal on computing (Print)  
Our technique is closely related to the notions of nearest-or farthest-neighbor generalized Voronoi diagrams, and of the union or intersection of geometric objects, where sharper bounds on the combinatorial  ...  ), the point of P farthest from ℓ can be computed in O * (n 1/2 ) time.  ...  The simplest solution is to adapt the technique of Aronov and Har-Peled [12] , which uses a procedure for answering range emptiness queries as a "black box".  ... 
doi:10.1137/090765092 fatcat:46hbmkx2ovfdtdqtwevodd4gdu

Intrinsic map dynamics exploration for uncharted effective free-energy landscapes

Eliodoro Chiavazzo, Roberto Covino, Ronald R. Coifman, C. William Gear, Anastasia S. Georgiou, Gerhard Hummer, Ioannis G. Kevrekidis
2017 Proceedings of the National Academy of Sciences of the United States of America  
We describe and implement a computer-assisted approach for accelerating the exploration of uncharted effective free-energy surfaces (FESs).  ...  The added value comes from biasing the simulator toward unexplored phase-space regions by exploiting the smoothness of the gradually revealed intrinsic low-dimensional geometry of the FES. free-energy  ...  ., and I.G.K. acknowledge the hospitality and support of the Institute for Advanced Study Technical University of Munich.  ... 
doi:10.1073/pnas.1621481114 pmid:28634293 pmcid:PMC5514710 fatcat:acqxlqlidnbp7izdmgvxkwmnh4

Approximating (k,ℓ)-center clustering for curves [article]

Kevin Buchin, Anne Driemel, Joachim Gudmundsson, Michael Horton, Irina Kostitsyna, Maarten Löffler, Martijn Struijs
2018 arXiv   pre-print
Finally, we observe that a careful adaptation of Gonzalez' algorithm in combination with a curve simplification yields a 3-approximation in any dimension, provided that an optimal simplification can be  ...  Given a set G of n points in Euclidean space, the problem is to determine a set C of k centers (not necessarily part of G) such that the maximum distance between a point in G and its nearest neighbor in  ...  Acknowledgements Natasja van de l'Isle is working on practical algorithms for curve clustering. We would like to thank her for sharing the example from Figure 1 with us.  ... 
arXiv:1805.01547v2 fatcat:j2t2v3ywwbfpdpejzy4tytho6y

DEF: Deep Estimation of Sharp Geometric Features in 3D Shapes [article]

Albert Matveev, Ruslan Rakhimov, Alexey Artemov, Gleb Bobrovskikh, Vage Egiazarian, Emil Bogomolov, Daniele Panozzo, Denis Zorin, Evgeny Burnaev
2022 arXiv   pre-print
We demonstrate a downstream application, where we reconstruct an explicit representation of straight and curved sharp feature lines from range scan data.  ...  Our approach is the first that scales to massive point clouds by fusing distance-to-feature estimates obtained on individual patches.  ...  Dzmitry Tsetserukou (Skoltech) and his laboratory staff for providing the 3D printing device and technical support.  ... 
arXiv:2011.15081v4 fatcat:xzk5urdppndkzpljtdvlgg5voq

Motion planning for an omnidirectional robot with steering constraints

Simon Chamberland, Éric Beaudry, Lionel Clavien, Froduald Kabanza, François Michaud, Michel Lauriay
2010 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems  
Our motion planner is based on a Rapidly-Exploring Random Trees (RRT) algorithm to sample the action space and find a feasible trajectory from an initial configuration to a goal configuration.  ...  One of the best approaches for a nonholonomic robot is to model the robot's velocity state as the motion around its instantaneous center of rotation (ICR).  ...  When the objective is to find a feasible solution as quickly as possible, the optimization heuristic (3) is not used and the algorithm rather relies on the standard exploration heuristic (2) .  ... 
doi:10.1109/iros.2010.5648987 dblp:conf/iros/ChamberlandBCKML10 fatcat:hdsusrjcxrg7zkhwydjbm4hzaq

Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics [article]

Tingran Gao, Shahar Z. Kovalsky, Doug M. Boyer, Ingrid Daubechies
2019 arXiv   pre-print
We provide a detailed exposition of numerical procedures and feature filtering algorithms for computing high-quality and semantically meaningful diffeomorphisms between disk-type anatomical surfaces.  ...  Daubechies, SIAM Journal on Mathematics of Data Science (2019)] to geometric morphometrics, a branch of evolutionary biology centered at the analysis and comparisons of anatomical shapes, and compares  ...  , Robert Ravier, and Shan Shan for assistance with collecting observer landmarks; the anonymous reviewers for many constructive feedback.  ... 
arXiv:1807.11887v3 fatcat:ukuyyvwnvzhuxmtli6uhirw2q4

Adaptive surrogate models for parametric studies [article]

Jan N. Fuhg
2019 arXiv   pre-print
The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative.  ...  In addition, an innovative adaptive scheme for binary classification is presented and tested for identifying chaotic motion of a Duffing's type oscillator.  ...  Determine the new sample point x (m+1) by utilizing the point in the cell farthest away from the corresponding cell sample point x sensitive . end Box 3.1 -Algorithm for CVVOR sample points for CV based  ... 
arXiv:1905.05345v1 fatcat:trwrcwf3vvgprad4he5n7hd76u

Semi-algebraic Range Reporting and Emptiness Searching with Applications [article]

Micha Sharir, Hayim Shaul
2009 arXiv   pre-print
In this paper we extend the analysis to general semi-algebraic ranges, and show how to adapt Matoušek's technique, without the need to linearize the ranges into a higher-dimensional space.  ...  As shown in Ma:rph, the two problems are closely related, and have solutions (for the case of halfspaces) with similar performance bounds.  ...  The simplest solution is to adapt the technique of Aronov and Har-Peled [12] , which uses a procedure for answering range emptiness queries as a "black box".  ... 
arXiv:0908.4061v2 fatcat:vewnmflbt5ajdg76qhncxsjfue

Clustering and Community Detection With Imbalanced Clusters

Cem Aksoylar, Jing Qian, Venkatesh Saligrama
2017 IEEE Transactions on Signal and Information Processing over Networks  
We present rigorous limit cut analysis results to justify our approach and demonstrate the superiority of our method through experiments on synthetic and real datasets for data clustering, semi-supervised  ...  Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, yielding a set of parameter dependent cuts reflecting varying levels of imbalance.  ...  To realize these cuts we parameterize a family of graphs over some parametric space λ ∈ Λ and generate candidate cuts using spectral methods as a black-box.  ... 
doi:10.1109/tsipn.2016.2601022 fatcat:s5r5bc5ytrbmrdrub5z45iuz2q
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