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When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance under Translation [article]

Karl Bringmann, Marvin Künnemann, André Nusser
2020 arXiv   pre-print
Perhaps the most natural such notion is the (discrete) Fréchet distance under translation.  ...  We combine these two ingredients to obtain an exact decision algorithm for the Fréchet distance under translation.  ...  Algorithm 1 Algorithm for deciding the Fréchet distance under translation.  ... 
arXiv:2008.07510v1 fatcat:fddnepz6vzcx5nu6yuobo2ersa

Protein Local Structure Alignment Under the Discrete Fréchet Distance

Binhai Zhu
2007 Journal of Computational Biology  
bounded discrete Fréchet distance it is NP-hard to approximate the maximum size common local structure within a factor of n 1 .  ...  A well-known measure to characterize the similarity of two polygonal chains is the famous Fréchet distance, and with the application of protein-related research, a related discrete Fréchet distance has  ...  Recently, Jiang et al. (2007) showed that the minimum discrete Fréchet distance between two chains in 2D, A and B, under translation can be computed in O.k 3 l 3 log.k C l // time, and under both translation  ... 
doi:10.1089/cmb.2007.0156 pmid:18052775 fatcat:vlhjnrdmf5batbqve2nusfy2vi

On the Complexity of Protein Local Structure Alignment Under the Discrete Fréchet Distance [article]

Binhai Zhu
2007 arXiv   pre-print
We show that given m proteins (or protein backbones, which are modeled as 3D polygonal chains each of length O(n)) the problem of protein local structure alignment under the discrete Fréchet distance is  ...  as hard as Independent Set.  ...  Recently, Jiang, et al. showed that the minimum discrete Fréchet distance between two chains in 2D, A and B, under translation can be computed in O(k 3 l 3 log(k+l))time, and under both translation and  ... 
arXiv:0709.0677v1 fatcat:lyjvsmwb4vbhvcnx5eg2i2wlem

When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance Under Translation

Karl Bringmann, Marvin Künnemann, André Nusser, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
Perhaps the most natural such notion is the (discrete) Fréchet distance under translation.  ...  We combine these two ingredients to obtain an exact decision algorithm for the Fréchet distance under translation.  ...  [5] together with an O(n 8 log n)-time algorithm. In this paper we focus on the discrete Fréchet distance under translation in the plane.  ... 
doi:10.4230/lipics.esa.2020.25 dblp:conf/esa/BringmannKN20 fatcat:26lwgipk6be7xla2rq3gt6q3u4

Voronoi Diagram of Polygonal Chains under the Discrete Fréchet Distance [article]

Sergey Bereg, Marina Gavrilova, Binhai Zhu
2007 arXiv   pre-print
In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension (d=2,3) under the discrete Frèchet distance.  ...  A well-known measure to characterize the similarity of two polygonal chains is the famous Frèchet distance.  ...  Acknowledgment We thank Minghui Jiang for pointing out the gap in an earlier version of the arguments for Theorem 3.3.  ... 
arXiv:0705.2835v1 fatcat:fu7qfxkix5gani4oewhmlryvea

VORONOI DIAGRAM OF POLYGONAL CHAINS UNDER THE DISCRETE FRÉCHET DISTANCE

SERGEY BEREG, KEVIN BUCHIN, MAIKE BUCHIN, MARINA GAVRILOVA, BINHAI ZHU
2010 International journal of computational geometry and applications  
In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension under the discrete Fréchet distance.  ...  A wellknown measure to characterize the similarity of two polygonal chains is the (continuous/discrete) Fréchet distance.  ...  Wong Education Foundation, Hong Kong and NSERC of Canada.  ... 
doi:10.1142/s0218195910003396 fatcat:tyooutrmtfchpiyd4ur2k3xmjq

A Practical Solution for Aligning and Simplifying Pairs of Protein Backbones under the Discrete Fréchet Distance [chapter]

Tim Wylie, Jun Luo, Binhai Zhu
2011 Lecture Notes in Computer Science  
In 2008, a problem called CPS-3F was proposed to simplify a pair of 3D chains simultaneously under the discrete Fréchet distance. However, it is still open whether CPS-3F is NP-complete or not.  ...  Recently, the discrete Fréchet distance has been applied to align and simplify protein backbones (geometrically, 3D polygonal chains) by Jiang et al., with insightful new results found.  ...  Acknowledgment This research is partially supported by NSF under grant DMS-0901034, by NSF of China under project 60928006, and by the Open Fund of Top Key Discipline of Computer Software and Theory in  ... 
doi:10.1007/978-3-642-21931-3_6 fatcat:e52gkxyajrayxb7smfq77ssp2u

Algorithms for the discrete Fréchet distance under translation

Omrit Filtser, Matthew Katz
2018
In 1D, we show how to avoid the use of parametric search and remove a logarithmic factor from the running time of (the 1D versions of) these algorithms and of an algorithm for the weak discrete \frechet  ...  Ben Avraham et al. (2015) presented an $O(m^3n^2(1+\log(n/m))\log(m+n))$-time algorithm for DFD between two sequences of points of sizes $m$ and $n$ in the plane under translation.  ...  DFDS under translation The discrete Fréchet distance (and its shortcuts variant) between A and B is determined by two points, one from A and one from B.  ... 
doi:10.20382/jocg.v11i1a7 fatcat:iloyepmywvajbl5iz5ynpshtg4

Fréchet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability [article]

Karl Bringmann, Marvin Künnemann, André Nusser
2021 arXiv   pre-print
in directed grid graphs suffices, and we solve this variant in amortized time Õ(N^1/3) per update, resulting in an improved running time of Õ(n^4.66...) for the discrete Fréchet distance under translation  ...  An important variant is the discrete Fréchet distance under translation, which enables detection of similar movement patterns in different spatial domains.  ...  Discrete Fréchet Distance Under Translation: Conditional Hardness and an Improved Algorithm 0:7 Line 7.  ... 
arXiv:1810.10982v4 fatcat:vigttzaebncczmlxrmtnbodg4y

Dynamic Time Warping Under Translation: Approximation Guided by Space-Filling Curves [article]

Karl Bringmann, Sándor Kisfaludi-Bak, Marvin Künnemann, Dániel Marx, André Nusser
2022 arXiv   pre-print
However, like the Fréchet distance, the DTW distance is not invariant under translations.  ...  Can we efficiently optimize the DTW distance of π and σ under arbitrary translations, to compare the curves' shape irrespective of their absolute location?  ...  Acknowledgements We thank Christian Wulff-Nilsen for making us aware of an improved offline dynamic shortest paths data structure.  ... 
arXiv:2203.07898v2 fatcat:gxnpbeainjbipiixopvluvreke

Translating Hausdorff is Hard: Fine-Grained Lower Bounds for Hausdorff Distance Under Translation [article]

Karl Bringmann, André Nusser
2022 arXiv   pre-print
As these bounds have not been improved for over 25 years, in this paper we approach the Hausdorff distance under translation from the perspective of fine-grained complexity theory.  ...  For point sets of size n and m, the Hausdorff distance under translation can be computed in time Õ(nm) for the L_1 and L_∞ norm [Chew, Kedem SWAT'92] and Õ(nm (n+m)) for the L_2 norm [Huttenlocher, Kedem  ...  The discrete Fréchet distance under translation has an Õ(n 4.66... )-time algorithm and a conditional lower bound of n 4−o (1) [9] , see also [10] for algorithm engineering work on this topic.  ... 
arXiv:2101.07696v5 fatcat:gc4nwusqjrgzlah7hfyvftfwvu

Face-to-Parameter Translation for Game Character Auto-Creation [article]

Tianyang Shi , Zhenwei Shi University of Michigan
2019 arXiv   pre-print
We formulate the above "artistic creation" process under a facial similarity measurement and parameter searching paradigm by solving an optimization problem over a large set of physically meaningful facial  ...  To effectively minimize the distance between the created face and the real one, two loss functions, i.e. a "discriminative loss" and a "facial content loss", are specifically designed.  ...  To quantitatively evaluate the similarity between the generated face and the in-game style reference, we use the Mode Score (MS) [43] and the Fréchet Inception Distance (FID) [18] as our metrics.  ... 
arXiv:1909.01064v1 fatcat:oee65xuwk5dvrckuk7r2fcfu6q

Frequency Domain Image Translation: More Photo-realistic, Better Identity-preserving [article]

Mu Cai, Hong Zhang, Huijuan Huang, Qichuan Geng, Yixuan Li, Gao Huang
2021 arXiv   pre-print
We broadly evaluate FDIT across five large-scale datasets and multiple tasks including image translation and GAN inversion.  ...  Image-to-image translation has been revolutionized with GAN-based methods. However, existing methods lack the ability to preserve the identity of the source domain.  ...  that FDIT can substantially improve the image quality while preserving the image content. We adopt the Fréchet Inception Distance (FID) [23] as the measure of image quality.  ... 
arXiv:2011.13611v3 fatcat:aamzkrmp5nbyfjxckruqyrcf2q

Efficient Nearest-Neighbor Query and Clustering of Planar Curves [article]

Boris Aronov, Omrit Filtser, Michael Horton, Matthew J. Katz, Khadijeh Sheikhan
2019 arXiv   pre-print
We use the well-known discrete Frechet distance function, both under L_∞ and under L_2, to measure the distance between two curves.  ...  We present near-linear time exact algorithms under L_∞, even when the location of the input curves is only fixed up to translation. Under L_2, we present a roughly O(n^2m^3)-time exact algorithm.  ...  Given a set of curves C as input, an optimal solution to the (1, 2)-Center problem under translation using the discrete Fréchet distance under the L ∞ metric can be computed in O(nm) time and O(nm) space  ... 
arXiv:1904.11026v1 fatcat:svwfs755anakla55m3rznhd2am

Global Curve Simplification [article]

Mees van de Kerkhof, Irina Kostitsyna, Maarten Löffler, Majid Mirzanezhad, Carola Wenk
2020 arXiv   pre-print
We provide polynomial-time algorithms for some variants of the global curve simplification problem and show NP-hardness for other variants.  ...  We consider six different curve distance measures: three variants of the Hausdorff distance and three variants of the Fréchet distance.  ...  Curve-restricted GCS under Discrete Fréchet Distance In this section we present an O(n 3 ) time algorithm for dF C (P, δ). Let P = p 1 , . . . , p n be a polygonal curve.  ... 
arXiv:1809.10269v2 fatcat:5qkpfs2bgbearg6opj3ltt6hzu
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