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Using R-Trees for Interactive Visualization of Large Multidimensional Datasets
[chapter]
2010
Lecture Notes in Computer Science
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Visualization interfaces are constrained in resolution and dimension, so cluttering and problems of projecting many dimensions into the available low dimensions are inherent. ...
bounding hyperboxes of internal R-tree nodes. ...
We thank our colleagues from the Institute of Data Analysis and Visualization (IDAV) at UC Davis. ...
doi:10.1007/978-3-642-17274-8_54
fatcat:sswx246gvvcnvawpwticlmj55u
Highway Dimension, Shortest Paths, and Provably Efficient Algorithms
[chapter]
2010
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
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We show that low highway dimension gives provable guarantees of efficiency for the following algorithms (sometimes with small modifications): reach (RE), contraction hierarchies (CH), highway hierarchies ...
We introduce the notion of highway dimension and show how low highway dimension gives a unified explanation for several seemingly different algorithms. ...
Acknowledgments We would like to thank Daniel Delling for suggesting the use of highway dimension in the analysis of the SHARC algorithm. ...
doi:10.1137/1.9781611973075.64
dblp:conf/soda/AbrahamFGW10
fatcat:7clqlztjo5hhfmerde3cuj4rwu
Collision detection for deforming necklaces
2002
Proceedings of the eighteenth annual symposium on Computational geometry - SCG '02
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In particular, we achieve an upper bound of O(n log n) in two dimensions and O(n 2−2/d ) in d-dimensions, d ≥ 3, for collision checking. ...
This hierarchy can be used for collision and self-collision detection. ...
Acknowledgments The authors wish to thank PankajAgarwal for his contributions to the results of this paper. Discussions with John Hershberger, Menelaos Karavelas, Rachel Kolodny, and Man-Cho A. ...
doi:10.1145/513400.513405
dblp:conf/compgeom/GuibasNRZ02
fatcat:g3jp753qdza6xi6ofjgmajp45m
A hierarchical method for real-time distance computation among moving convex bodies
2000
Computational geometry
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For convex polygons, we prove that H-Walk improves on the classic Lin-Canny and Dobkin-Kirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. ...
If the time step is small enough, the closest pair of features (vertices, edges or faces) between two polyhedra will not move very far from one time step to the next. ...
Acknowledgements We would like to thank Brian Mirtich for helpful discussion of the collision detection problem and for providing us an implementation for the V-Clip algorithm. ...
doi:10.1016/s0925-7721(99)00042-5
fatcat:ylgvqqxjgbarjbly4lrtek6jly
W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications
[chapter]
2005
Lecture Notes in Computer Science
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The notion of linear fpt-reductions has been recently used to derive strong computational lower bounds for well-known NP-hard problems. ...
In this paper, we formally investigate the notions of W [t]-hardness and W [t]-completeness under the linear fpt-reduction, and study structural properties of the corresponding complexity classes. ...
class logsnp, and that v-c dimension is complete under the polynomial time reduction for the class lognp. ...
doi:10.1007/11533719_98
fatcat:ewojc2i2z5gbllf6ynfulngu2a
H-Walk
1999
Proceedings of the fifteenth annual symposium on Computational geometry - SCG '99
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For convex polygons, we prove that H-Walk improves on the classic Lin-Canny and Dobkin-Kirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. ...
This paper presents the Hierarchical Walk, or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. ...
Acknowledgment We would like to thank Brian Mirtich for helpful discussion of the collision detection problem and for providing us an implementation for the V-Clip algorithm. ...
doi:10.1145/304893.304979
dblp:conf/compgeom/GuibasHZ99
fatcat:wkw554g4bfgyjkyr2yrl2gb4gy
Deep Hierarchical Super-Resolution for Scientific Data Reduction and Visualization
[article]
2021
arXiv
pre-print
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We train a hierarchy of neural networks, each capable of 2x upscaling in each spatial dimension between two levels of detail, and use these networks in tandem to facilitate large scale factor super resolution ...
We present an approach for hierarchical super resolution (SR) using neural networks on an octree data representation. ...
, O(DS) is the time complexity for the downscaling algorithm, and O(SR) is the time complexity for the super resolution algorithm. ...
arXiv:2107.00462v1
fatcat:37qe5d6v4bgrzb3cy5fnzf2qjm
Hierarchical Heavy Hitters with the Space Saving Algorithm
[article]
2011
arXiv
pre-print
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It improves on the worst-case time and space bounds of earlier algorithms, is conceptually simple and substantially easier to implement, offers improved accuracy guarantees, is easily adopted to a distributed ...
in terms of space, while our one-dimensional algorithm is also superior in terms of speed and accuracy for a more limited range of parameters. ...
We thank Elaine Angelino, Richard Bates, and Graham Cormode for helpful discussions. ...
arXiv:1102.5540v2
fatcat:2exoilbqwnfihnaac44edms6aa
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms
[article]
2015
arXiv
pre-print
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In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension and diameter for the current fastest routing algorithms, including contraction hierarchies, transit ...
We also show how to improve a result by Milosavljevic which lower bounds the number of shortcuts added in the preprocessing stage for contraction hierarchies. ...
We would like to give a huge thanks to Lyle McGeoch for helpful discussions and suggestions throughout the writing process. We are grateful for the Post-Baccalaureate ...
arXiv:1501.04262v2
fatcat:42p7ddv3n5eszl3v47lfhx7bum
Sharp metastability threshold for an anisotropic bootstrap percolation model
2013
Annals of Probability
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At each time step, sites that are occupied remain occupied, while sites that are not occupied become occupied if and only if three of more sites in their neighborhood are occupied. ...
At time 0, sites are occupied with probability p. ...
The first author would like to thank Stanislav Smirnov for his constant support. ...
doi:10.1214/11-aop722
fatcat:ogmteyvftrg6rfrc2e2ltieyty
Finding hierarchical heavy hitters in streaming data
2008
ACM Transactions on Knowledge Discovery from Data
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Data items that arrive online as streams typically have attributes which take values from one or more hierarchies (time and geographic location; source and destination IP addresses; etc.). ...
Our algorithms exploit this structure, and so are able to to track approximate HHHs using only a small, fixed number of statistics per stored item, regardless of the number of dimensions. ...
For two dimensions, we have a product of hierarchies. ...
doi:10.1145/1324172.1324174
fatcat:drdnstmp2nde7mhf3yisejx6lu
Brane World Confronts Holography
[article]
2004
arXiv
pre-print
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We discuss the implications for extra dimensions as well as holography. ...
The thermodynamic entropy of astrophysical black holes and sub-horizon volumes during big bang nucleosynthesis exceed the relevant bounds unless M_* > 10^(4-6) TeV, so a hierarchy relative to the weak ...
INTRODUCTION The idea that our universe might have extra dimensions beyond four space-time dimensions dates long back to early last century. ...
arXiv:hep-th/0401060v1
fatcat:whakeopsdnbj3ismbxqsayzmjq
Collision detection for deforming necklaces*1
2004
Computational geometry
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Using this hierarchy, we achieve a collision detection upper bound of O(n log n) in two dimensions and O(n 2−2/d ) in d-dimensions, d 3. ...
In particular, we study a bounding volume hierarchy based on spheres which can be used for collision and self-collision detection of deforming and moving necklaces. ...
Acknowledgements The authors wish to thank John Hershberger, Menelaos Karavelas, Rachel Kolodny, and Antony So for their helpful discussions and Erik Lindhahl for the molecular simulation data. ...
doi:10.1016/s0925-7721(04)00027-6
fatcat:s6bi6mizfbgr3oc6nnzmac4foi
Collision detection for deforming necklaces
2004
Computational geometry
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Using this hierarchy, we achieve a collision detection upper bound of O(n log n) in two dimensions and O(n 2−2/d ) in d-dimensions, d 3. ...
In particular, we study a bounding volume hierarchy based on spheres which can be used for collision and self-collision detection of deforming and moving necklaces. ...
Acknowledgements The authors wish to thank John Hershberger, Menelaos Karavelas, Rachel Kolodny, and Antony So for their helpful discussions and Erik Lindhahl for the molecular simulation data. ...
doi:10.1016/j.comgeo.2004.03.008
fatcat:usdp2fuj5vh5jktnc3z66mvhma
Subquadratic encodings for point configurations
2019
Journal of Computational Geometry
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Finally, we generalize our results to the encoding of point configurations in higher dimension. ...
\(O(\log n)\) time in the word-RAM model with word size \(w \geq \log n\). ...
Correctness and Query Complexity As before, a query is answered by traversing the hierarchy, which takes O(log n) time. ...
doi:10.20382/jocg.v10i2a6
dblp:journals/jocg/CardinalCILO19
fatcat:lj3ldokeo5gm7l2sbh55nesnvy
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