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Computing Height-Optimal Tangles Faster
[article]
2019
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2006
arXiv
pre-print
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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
2007
Journal of knot theory and its ramifications
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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]
2014
arXiv
pre-print
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2013
2013 IEEE Second International Conference on Image Information Processing (ICIIP-2013)
unpublished
doi:10.1109/iciip.2013.6707551 fatcat:ujljvsnmifa2fbbqakanlzzwiq
doi:10.1109/iciip.2013.6707551 fatcat:ujljvsnmifa2fbbqakanlzzwiq
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]
2011
Proceedings of the 20th International Meshing Roundtable
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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
2009
Computers & graphics
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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]
2005
Emerging Theory, Methods, and Applications
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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]
2019
arXiv
pre-print
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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?
2021
Sensors
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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
2010
ACM Transactions on Graphics
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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
2016
Computer-Aided Design
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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
1996
ACM Computing Surveys
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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
2004
Information Processing Letters
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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
2002
IEEE Transactions on Robotics and Automation
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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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