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Parameterization Above a Multiplicative Guarantee

Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi, Michael Wagner
2020 Innovations in Theoretical Computer Science  
Parameterization above a guarantee is a successful paradigm in Parameterized Complexity.  ...  We highlight a multiplicative form of parameterization above a guarantee: Given an instance (I, k) of some (parameterized) problem Π with a guarantee g(I), decide whether I admits a solution of size at  ...  Multiplicative Above Guarantee Parameterization To the best of our knowledge, all successful above guarantee parameterizations are additive.  ... 
doi:10.4230/lipics.itcs.2020.39 dblp:conf/innovations/FominGLP0Z20 fatcat:soqaonrddjeoljfyc6ce24s3ae

A Survey on Graph Problems Parameterized Above and Below Guaranteed Values [article]

Gregory Gutin, Matthias Mnich
2022 arXiv   pre-print
We survey the field of algorithms and complexity for graph problems parameterized above or below guaranteed values, a research area which was pioneered by Venkatesh Raman.  ...  Those problems seek, for a given graph G, a solution whose value is at least g(G)+k or at most g(G)-k, where g(G) is a guarantee on the value that any solution on G takes.  ...  Section 3 briefly describes results and an open problem on two above-guarantee (additive and multiplicative) parameterizations of the Minimum Arrangement problem and on two additive above-guarantee parameterization  ... 
arXiv:2207.12278v1 fatcat:va33yl356fh5xn64qge6tvhpuq

Surface Creation and Curve Deformations Between Two Complex Closed Spatial Spline Curves [chapter]

Joel Daniels, Elaine Cohen
2006 Lecture Notes in Computer Science  
This is achieved in a manner that assures there will be neither singularities in the parameterization nor self-intersections in the projected surface.  ...  We describe an algorithm that generates a temporal deformation between the input curves, one which can be thought of as sweeping a surface.  ...  The uniqueness theorem guarantees that all seeds dropped within V will trace non-intersecting paths.  ... 
doi:10.1007/11802914_16 fatcat:z2ebbqz5brgfvixe6tbph7rhkm

Median and Mode Ellipse Parameterization for Robust Contour Fitting [article]

Michael A. Greminger
2015 arXiv   pre-print
This article introduces a new curve parameterization algorithm that is able to fit a closed curve to a set of points while being robust to the presence of outliers and occlusions in the data.  ...  The closed curve is parameterized by determining the median perimeter of the set of ellipses. The resulting curve is not an ellipse, allowing arbitrary closed contours to be parameterized.  ...  As discussed above, 0 can be guaranteed with median ellipse parameterization.  ... 
arXiv:1504.05623v1 fatcat:vgubnkpwxbfv7oq4wqyoihrora

Bijective parameterization with free boundaries

Jason Smith, Scott Schaefer
2015 ACM Transactions on Graphics  
Surface parameterization generates a correspondence, or mapping, between the 3D surface and 2D parameterization space. This mapping has many applications in computer x  ...  If the error is above a specified threshold, charts could be split into multiple pieces similar to [26] or [63] and re-optimized using the bijective approach.  ...  If the parameterization is not bijective, then a single point in the texture could map to multiple, disconnected While only a handful of previous methods guarantee that the parameterization will be locally  ... 
doi:10.1145/2766947 fatcat:vdpxvrpvp5aczcqrs7ahljhe7e

Cross-parameterization and compatible remeshing of 3D models

Vladislav Kraevoy, Alla Sheffer
2004 ACM SIGGRAPH 2004 Papers on - SIGGRAPH '04  
Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints.  ...  In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing.  ...  The parameterization method is guaranteed to find a bijective, feature-preserving parameterization for any set of models.  ... 
doi:10.1145/1186562.1015811 fatcat:euz5fcw4rvczvhv5alxyrtkn4a

Cross-parameterization and compatible remeshing of 3D models

Vladislav Kraevoy, Alla Sheffer
2004 ACM Transactions on Graphics  
Our crossparameterization method computes a low-distortion bijective mapping between models that satisfies user prescribed constraints.  ...  In this paper we introduce novel methods for shape preserving cross-parameterization and compatible remeshing.  ...  The parameterization method is guaranteed to find a bijective, feature-preserving parameterization for any set of models.  ... 
doi:10.1145/1015706.1015811 fatcat:pkczt4zb4bcpddtx7rliyoyds4

Mesh Parameterization Methods and Their Applications

Alla Sheffer, Emil Praun, Kenneth Rose
2006 Foundations and Trends in Computer Graphics and Vision  
Planar Mesh Embedding 119 Parameterization with uniform weights [128] on a circular domain. Parameterization with harmonic weights [28] on a circular domain.  ...  This survey focuses on the practical aspects of the methods available, such as time complexity and robustness and shows multiple examples of parameterizations generated using different methods, allowing  ...  First, a mesh is parameterized using one of the existing techniques listed above, and then a second, post-processing stage is applied to improve the parameterization.  ... 
doi:10.1561/0600000011 fatcat:k3vrqx4s2bgmrmivetwsc5nhqm

A Design Method for Modified PID Controllers for Multiple-Input/Multiple-Output Plants

Takaaki HAGIWARA, Kou YAMADA, Shun MATSUURA, Satoshi AOYAMA
2012 Journal of System Design and Dynamics  
Recently, the parameterization of all stabilizing PID controllers has been considered. This method obtains admissible sets of PID parameters to guarantee the stability of a closed-loop system.  ...  However, no method has been published that can guarantee the stability of PID control systems for multiple-input/multiple-output plants, or find admissible sets of P-parameters, I-parameters and D-parameters  ...  The parameterization of all stabilizing controllers for multiple-input/multiple-output plants includes a free parameter.  ... 
doi:10.1299/jsdd.6.131 fatcat:fucmzc6ztjgn7hk4ztkh4jke2i

A randomized approach to the H/sub 2//H/sub /spl infin// control problem via Q-parameterization

K.R. Horspool, R.S. Erwin, C. Abdallah, P. Dorato
2000 Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)  
Q-parameterization provides a mechanism to search over all stabilizing controllers, and thus gives us the ability to search for H2 minimizing controllers, while still providing stability robustness.  ...  With very little modification, we are able to deal with multiple objectives, plant uncertainty, and fixed order controllers.  ...  Furthermore, if the conditions of the follwoing theorem are met, it is guaranteed that Q parameterizes all robustly stabilizing controllers.  ... 
doi:10.1109/acc.2000.876731 fatcat:dxplvzh4pfdxlp5enmqwhawlpm

Controller parameterization for SISO and MIMO plants with time delay

Weidong Zhang, Frank Allgower, Tao Liu
2006 Systems & control letters (Print)  
Controller parameterization is a very fundamental problem in control theory.  ...  A new parameterization is derived on the basis of the definition of the internal stability.  ...  Weidong Zhang was a Humboldt Research Fellow at the IST of the University of Stuttgart with Prof. Dr.-Ing F. Allgower.  ... 
doi:10.1016/j.sysconle.2006.03.008 fatcat:k3hpyddav5awvg5cfrtpigbml4

Consistent mesh parameterizations

Emil Praun, Wim Sweldens, Peter Schröder
2001 Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01  
Abstract A basic element of Digital Geometry Processing algorithms is the establishment of a smooth parameterization for a given model.  ...  In this paper we propose an algorithm which establishes parameterizations for a set of models.  ...  DGP algorithms involving multiple models require a common parameterization and a common sampling pattern.  ... 
doi:10.1145/383259.383277 dblp:conf/siggraph/PraunSS01 fatcat:lvnt3lyp6vge3g32qd3wekds6i

Restructuring expression dags for efficient parallelization [article]

Martin Wilhelm
2018 arXiv   pre-print
We compare the impact of several restructuring methods for the expression dag on its running time in a parallel environment.  ...  We show that exact-decisions number types based on expression dags can be evaluated faster in practice through parallelization on multiple cores.  ...  If a division node is passed while the counter is still smaller than the threshold, the counter is reset to zero, since then the additions and subtractions above the division node cause additional multiplications  ... 
arXiv:1804.03256v1 fatcat:cp57mmdw6zcober4j74zbb5c6q

Parameterization of Faceted Surfaces for Meshing using Angle-Based Flattening

A. Sheffer, E. de Sturler
2001 Engineering with Computers  
We propose a new method to compute planar triangulations of faceted surfaces for surface parameterization.  ...  We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.  ...  Multiple approaches for parameterization of tessellated surfaces have been suggested. McCartney et al. [9] suggest a heuristic approach for triangulation flattening.  ... 
doi:10.1007/pl00013391 fatcat:2qjasz4guzbo3axbttdg3eowai

Integrable PolyVector fields

Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung
2015 ACM Transactions on Graphics  
We present a framework for designing curl-free tangent vector fields on discrete surfaces.  ...  Such vector fields are gradients of locallydefined scalar functions, and this property is beneficial for creating surface parameterizations, since the gradients of the parameterization coordinate functions  ...  Multiple scalar parameterization functions A mesh parameterization is a pair of scalar functions (u, v) : V → R 2 representing the mapping between surface points and points on a plane.  ... 
doi:10.1145/2766906 fatcat:7ughmo3wkbah3jtgqjkgrd7uqu
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