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Computing Height-Optimal Tangles Faster [article]

Oksana Firman, Philipp Kindermann, Alexander Ravsky, Alexander Wolff, Johannes Zink
2019 arXiv   pre-print
We show that this problem is NP-hard, and we give an algorithm that computes an optimal tangle for n wires and a given list L of swaps in O((2|L|/n^2+1)^n^2/2·φ^n · n) time, where φ≈ 1.618 is the golden  ...  The aim is to find a tangle that realizes L using the smallest number of layers.  ...  A tangle T is optimal if h(T ) = h(L(T )). In the Tangle-Height Minimization problem, we are given a swap list L and the goal is to compute an optimal tangle T realizing L.  ... 
arXiv:1901.06548v5 fatcat:3ubpsd53mnb4bgbq7y3lzprjqi

The Complexity of Finding Tangles [article]

Oksana Firman, Stefan Felsner, Philipp Kindermann, Alexander Ravsky, Alexander Wolff, Johannes Zink
2020 arXiv   pre-print
Finding a tangle that realizes a given multiset of swaps and uses the least number of layers is known to be NP-hard. We show that it is even NP-hard to decide if a realizing tangle exists.  ...  Given a set of n y-monotone curves, which we call wires, a tangle determines the order of the wires on a number of horizontal layers such that the orders of the wires on any two consecutive layers differ  ...  Can we decide the feasibility of a list faster than finding its optimal realization?  ... 
arXiv:2002.12251v1 fatcat:tinelr5huvdxbonn74kpoxnmia

Fast Khovanov Homology Computations [article]

Dror Bar-Natan
2006 arXiv   pre-print
We introduce a local algorithm for Khovanov Homology computations - that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a ("local") tangle, hence canceling  ...  This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups that otherwise would have taken centuries to evaluate.  ...  Then in Section 7 we describe in even faster variant of the algorithm and in Section 8 we mention the two available implementations and exhibit a sample computation.  ... 
arXiv:math/0606318v1 fatcat:5fqgoj3ksbdmjaublwrzjpafk4

FAST KHOVANOV HOMOLOGY COMPUTATIONS

DROR BAR-NATAN
2007 Journal of knot theory and its ramifications  
We introduce a local algorithm for Khovanov Homology computations -that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a ("local") tangle, hence canceling the  ...  This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups that otherwise would have taken centuries to evaluate.  ...  Then in Section 7 we describe an even faster variant of the algorithm and in Section 8 we mention the two available implementations and exhibit a sample computation.  ... 
doi:10.1142/s0218216507005294 fatcat:kr7wlugqijdifi7inp4jduyjpi

Use of Computer Vision to Detect Tangles in Tangled Objects [article]

Paritosh Parmar
2014 arXiv   pre-print
This paper proposes a computer vision based method for analyzing visual data acquired from camera for perceiving the overlap of wires, ropes, hoses i.e. detecting tangles.  ...  This problem can be tackled by using computer vision system in robot.  ...  However, parallelizing this method can make this method faster. Fig. 1 . 1 Tangle/overlap indicated in a tangled mass of wire (left). Tangled mass of wires (right).  ... 
arXiv:1405.4802v1 fatcat:j66ezlyh5rc7tbfbmn2zuylceq

Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation [chapter]

Xevi Roca, Abel Gargallo-Peiró, Josep Sarrate
2011 Proceedings of the 20th International Meshing Roundtable  
The final goal is to obtain the wave amplification factor for an incident wave of height one.  ...  Therefore, several tangled elements appear at the inner boundary.  ... 
doi:10.1007/978-3-642-24734-7_20 dblp:conf/imr/RocaGS11 fatcat:6xczymbe5fe5bp4clnqhwna3rq

Quality encoding for tetrahedral mesh optimization

Kai Xu, Zhi-Quan Cheng, Yanzhen Wang, Yueshan Xiong, Hao Zhang
2009 Computers & graphics  
We develop an algorithm for tetrahedral mesh optimization through energy minimization driven by QDC.  ...  To ensure quality boundary of the resulting tetrahedral mesh, we propose a harmonic-guided optimization scheme which leads to consistent handling of both the interior and boundary tetrahedra.  ...  Generally, all-vertex approaches have faster convergence rate and often provide more accurate optimization results than single-vertex ones, although they need more computation for a single iteration [  ... 
doi:10.1016/j.cag.2009.03.020 fatcat:epc3iaqpwvhdxmcdbcbd4gpl7a

Branch and Tree Decomposition Techniques for Discrete Optimization [chapter]

Illya V. Hicks, Arie M. C. A. Koster, Elif Kolotoğlu
2005 Emerging Theory, Methods, and Applications  
This chapter gives a general overview of two emerging techniques for discrete optimization that have footholds in mathematics, computer science, and operations research: branch decompositions and tree  ...  The algorithmic importance of branch decompositions and tree decompositions for solving NP-hard problems modelled on graphs was first realized by computer scientists in relation to formulating graph problems  ...  DMI-0217265), the DFG research group "Algorithms, Structure, Randomness" (grant GR 883/9-3, GR 883/9-4), and the Netherlands Organization for Scientific Research (project Treewidth and Combinatorial Optimization  ... 
doi:10.1287/educ.1053.0017 fatcat:czyk6fbzdre53cp4zxfyckd5ga

Improving Strong-Scaling of CNN Training by Exploiting Finer-Grained Parallelism [article]

Nikoli Dryden, Naoya Maruyama, Tom Benson, Tim Moon, Marc Snir, Brian Van Essen
2019 arXiv   pre-print
Our algorithms allow us to prototype a model for a mesh-tangling dataset, where sample sizes are very large.  ...  Experiments were performed at the Livermore Computing facility. The authors thank the LBANN and Alkemi teams for their assistance.  ...  In this work, we focus on cluster systems with NVIDIA GPUs as the main computing platform for training and use NVIDIA's cuDNN library for optimized compute kernels.  ... 
arXiv:1903.06681v1 fatcat:jdqckhwylvamvhda6b6bzqszry

Threat Modeling—How to Visualize Attacks on IOTA?

Ikram Ullah, Gerard de de Roode, Nirvana Meratnia, Paul Havinga
2021 Sensors  
Figure 3 . 3 Weight, cumulative weight and score in the tangle. Figure 4 . 4 Height and depth in the tangle. Figure 5 . 5 Adding a transaction to the tangle.  ...  looks like to optimally execute the attack [72] .  ... 
doi:10.3390/s21051834 pmid:33800712 pmcid:PMC7975986 fatcat:spw47bipbrbito5vpqfqratfse

Spatial relationship preserving character motion adaptation

Edmond S. L. Ho, Taku Komura, Chiew-Lan Tai
2010 ACM Transactions on Graphics  
It also works well for interactions involving contacts and tangles as well as those without any contacts. The method is computationally efficient, allowing real-time character control.  ...  Since most of the computation, such as the computation of the Laplacian and constraint matrices and solving the large linear system [Bolz et al. 2003 ] are highly parallelizable, much faster response  ...  Ho and Komura [2009b] use Gauss Linking Integral to detect tangled limbs and encode them using rational tangles for motion retrieval.  ... 
doi:10.1145/1778765.1778770 fatcat:6452x2nr5fdpvj5lploceir6ce

Implementation and evaluation of automated tetrahedral–prismatic mesh generation software

David Eller, Maximilian Tomac
2016 Computer-Aided Design  
Satisfactory mesh quality is demonstrated by comparing solutions obtained using the new meshes with reference data computed on high-quality advancing-front grids.  ...  The method employed combines the established, and very fast, Delaunay-based tetrahedral mesh generator TetGen with a novel technique for the creation of a prismatic layer, where constrained global optimization  ...  This process is substantially faster at just below 2 hours, but does not result in a mesh which passes the pre-processor of the Edge flow solver due to tangled or inverted cells.  ... 
doi:10.1016/j.cad.2015.06.010 fatcat:rxmsmgzehvbcxmnlbzig45f2fy

Aspect-oriented programming

G. Kiczales
1996 ACM Computing Surveys  
This forces the implementation of those design decisions to be scattered throughout the code, resulting in "tangled" code that is excessively difficult to develop and maintain.  ...  Optimizing Memory Usage But this simple implementation doesn't address the second goal of optimizing memory usage.  ...  The clean implementation of the real system, similar to the first code shown above, is only 768 lines of code; but the tangled implementation, which does the fusion optimization as well as memoization  ... 
doi:10.1145/242224.242420 fatcat:c5utw54ezjgwbllhfx3lh2oku4

Exhaustive approaches to 2D rectangular perfect packings

N. Lesh, J. Marks, A. McMahon, M. Mitzenmacher
2004 Information Processing Letters  
The goal is to pack the rectangles without overlap into a single rec-tangle of width W and minimum height H .  ...  As typical of experimental work, we expect the code could be optimized to run much faster. We were significantly aided by the solutionrichness of the instances.  ... 
doi:10.1016/j.ipl.2004.01.006 fatcat:4nmzonwxe5h2nmqujzb7d2basi

Interference-free polyhedral configurations for stacking

V.R. Ayyadevara, D.A. Bourne, K. Shimada, R.H. Sturges
2002 IEEE Transactions on Robotics and Automation  
The second technique computes near optimal interference-free positions for a discrete orientation without having to compute the complete -space obstacle.  ...  The cost function is a weighted sum of components that penalize floor space utilization and height of center of gravity of parts.  ...  This again would help us compute interference-free configurations faster without sacrificing solution quality.  ... 
doi:10.1109/tra.2002.999644 fatcat:iqdp2isl5fazvfvxmd57wp7pqa
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