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Computing Height-Optimal Tangles Faster
[article]

2019
*
arXiv
*
pre-print

We show that this problem is NP-hard, and we give an algorithm that

arXiv:1901.06548v5
fatcat:3ubpsd53mnb4bgbq7y3lzprjqi
*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. ...##
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The Complexity of Finding Tangles
[article]

2020
*
arXiv
*
pre-print

Finding a

arXiv:2002.12251v1
fatcat:tinelr5huvdxbonn74kpoxnmia
*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? ...##
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Fast Khovanov Homology Computations
[article]

2006
*
arXiv
*
pre-print

We introduce a local algorithm for Khovanov Homology

arXiv:math/0606318v1
fatcat:5fqgoj3ksbdmjaublwrzjpafk4
*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*. ...##
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FAST KHOVANOV HOMOLOGY COMPUTATIONS

2007
*
Journal of knot theory and its ramifications
*

We introduce a local algorithm for Khovanov Homology

doi:10.1142/s0218216507005294
fatcat:kr7wlugqijdifi7inp4jduyjpi
*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*. ...##
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Use of Computer Vision to Detect Tangles in Tangled Objects
[article]

2014
*
arXiv
*
pre-print

This paper proposes a

arXiv:1405.4802v1
fatcat:j66ezlyh5rc7tbfbmn2zuylceq
*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). ...##
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Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation
[chapter]

2011
*
Proceedings of the 20th International Meshing Roundtable
*

The final goal is to obtain the wave amplification factor for an incident wave of

doi:10.1007/978-3-642-24734-7_20
dblp:conf/imr/RocaGS11
fatcat:6xczymbe5fe5bp4clnqhwna3rq
*height*one. ... Therefore, several*tangled*elements appear at the inner boundary. ...##
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Quality encoding for tetrahedral mesh optimization

2009
*
Computers & graphics
*

We develop an algorithm for tetrahedral mesh

doi:10.1016/j.cag.2009.03.020
fatcat:epc3iaqpwvhdxmcdbcbd4gpl7a
*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 [ ...##
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Branch and Tree Decomposition Techniques for Discrete Optimization
[chapter]

2005
*
Emerging Theory, Methods, and Applications
*

This chapter gives a general overview of two emerging techniques for discrete

doi:10.1287/educ.1053.0017
fatcat:czyk6fbzdre53cp4zxfyckd5ga
*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*...##
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Improving Strong-Scaling of CNN Training by Exploiting Finer-Grained Parallelism
[article]

2019
*
arXiv
*
pre-print

Our algorithms allow us to prototype a model for a mesh-

arXiv:1903.06681v1
fatcat:jdqckhwylvamvhda6b6bzqszry
*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. ...##
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Threat Modeling—How to Visualize Attacks on IOTA?

2021
*
Sensors
*

Figure 3 . 3 Weight, cumulative weight and score in the

doi:10.3390/s21051834
pmid:33800712
pmcid:PMC7975986
fatcat:spw47bipbrbito5vpqfqratfse
*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] . ...##
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Spatial relationship preserving character motion adaptation

2010
*
ACM Transactions on Graphics
*

It also works well for interactions involving contacts and

doi:10.1145/1778765.1778770
fatcat:6452x2nr5fdpvj5lploceir6ce
*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. ...##
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Implementation and evaluation of automated tetrahedral–prismatic mesh generation software

2016
*
Computer-Aided Design
*

Satisfactory mesh quality is demonstrated by comparing solutions obtained using the new meshes with reference data

doi:10.1016/j.cad.2015.06.010
fatcat:rxmsmgzehvbcxmnlbzig45f2fy
*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. ...##
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Aspect-oriented programming

1996
*
ACM Computing Surveys
*

This forces the implementation of those design decisions to be scattered throughout the code, resulting in "

doi:10.1145/242224.242420
fatcat:c5utw54ezjgwbllhfx3lh2oku4
*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 ...##
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Exhaustive approaches to 2D rectangular perfect packings

2004
*
Information Processing Letters
*

The goal is to pack the rectangles without overlap into a single rec-

doi:10.1016/j.ipl.2004.01.006
fatcat:4nmzonwxe5h2nmqujzb7d2basi
*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. ...##
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Interference-free polyhedral configurations for stacking

2002
*
IEEE Transactions on Robotics and Automation
*

The second technique

doi:10.1109/tra.2002.999644
fatcat:iqdp2isl5fazvfvxmd57wp7pqa
*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. ...
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