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When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance under Translation
[article]
2020
arXiv
pre-print
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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
2007
Journal of Computational Biology
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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]
2007
arXiv
pre-print
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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
2020
European Symposium on Algorithms
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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]
2007
arXiv
pre-print
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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
2010
International journal of computational geometry and applications
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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]
2011
Lecture Notes in Computer Science
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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
2018
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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]
2021
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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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