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Competitive Online Searching for a Ray in the Plane

Andrea Eubeler, Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, Gerhard Trippen, Sándor Fekete, Alejandro Lopez-Ortiz
2007
Our strategy achieves a competitive factor of $1.059ldots$, which is optimal. Then, we consider rays in arbitrary position in the plane.  ...  First, we give a search strategy for a special case of the ray search---the window shopper problem---, where the ray we are looking for is perpendicular to a known ray.  ...  . , 1) (0, 0) (b, 0) 0, 1−b 2 2 b, 1−b 2 Searching for a Ray in the Plane In this section, we consider the general problem of searching for the origin of a ray in the plane.  ... 
doi:10.4230/dagsemproc.06421.5 fatcat:gyterc5oyrhstbmwf5kfyg6ahi

Lower Bounds for Shoreline Searching With 2 or More Robots

Sumi Acharjee, Konstantinos Georgiou, Somnath Kundu, Akshaya Srinivasan, Michael Wagner
2020 International Conference on Principles of Distributed Systems  
Searching for a line on the plane with n unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every n ≥ 1, see [5] .  ...  In this work we improve the best lower bound known for n = 2 robots [5] from 1.5993 to 3.  ...  Finally, the very recent [31] studied cost/information trade-offs for searching in the plane for a point.  ... 
doi:10.4230/lipics.opodis.2019.26 dblp:conf/opodis/AcharjeeGKS19 fatcat:y7wqjcwbf5hobckmb2fbh3darq

Lower Bounds for Shoreline Searching with 2 or More Robots [article]

Sumi Acharjee, Konstantinos Georgiou, Somnath Kundu, Akshaya Srinivasan
2020 arXiv   pre-print
Searching for a line on the plane with n unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every n≥ 1.  ...  In this work we improve the best lower bound known for n=2 robots from 1.5993 to 3.  ...  Finally, the very recent [31] studied cost/information trade-offs for searching in the plane for a point.  ... 
arXiv:2001.04311v1 fatcat:txoyjuca45bzblizcfsrrrcwbe

Wireless Evacuation on m Rays with k Searchers [chapter]

Sebastian Brandt, Klaus-Tycho Foerster, Benjamin Richner, Roger Wattenhofer
2017 Lecture Notes in Computer Science  
We study the online problem of evacuating k robots on m concurrent rays to a single unknown exit.  ...  For k = 3 robots on m = 3 rays, we give a class of parametrized algorithms with a nearly matching competitive ratio of 2 + √ 3 ≈ 3.73205.  ...  We would also like to thank the anonymous reviewers of this journal article for their helpful comments on our submission.  ... 
doi:10.1007/978-3-319-72050-0_9 fatcat:i7rmy7jkjbcxrbcmdrapxlbqde

Page 5401 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
At ‘time’ t, the lines of sight are parallel to the ray r(t) in the plane P, which starts in the origin of P and represents the angle a(t) (orthographic views of the scene).  ...  The diameter result yields a fast implementation of the greedy heuristic for maximum-weight Euclidean matching and an efficient online algorithm to maintain approximate convex hulls in the plane.”  ... 

Optimal Online Escape Path Against a Certificate

Elmar Langetepe, David Kübel, Marc Herbstritt
2016 Scandinavian Workshop on Algorithm Theory  
For a class of environments (convex shapes and shapes with kernel positions) we design an online strategy that always leaves the environment.  ...  Because of this, in the above convex examples the certificate path always (for any position s) leaves the environment earlier than the ultimate escape path.  ...  We would like to thank the anonymous referees for their helpful comments and suggestions.  ... 
doi:10.4230/lipics.swat.2016.19 dblp:conf/swat/LangetepeK16 fatcat:6vdxzew2ezcctcyzhech65vefm

Online algorithms for searching and exploration in the plane

Subir Kumar Ghosh, Rolf Klein
2010 Computer Science Review  
Klein, Online algorithms for searching and exploration in the plane, Computer Science Review, 4:189-201, 2010. 2. P.  ...  Searching for a target on m rays 0 1 2 4 R O t A beautiful young cow Ariadne is at the entrance of a simple labyrinth which branches in m ≥ 2 corridors.  ...  Exploring unknown polygons: discrete visibility In the remaining part of the lecture, we present exploration algorithms and their competitive ratios from the following papers.  ... 
doi:10.1016/j.cosrev.2010.05.001 fatcat:wqfwuhzelnfzhg2kgc7ditb4em

Optimal online escape path against a certificate [article]

Elmar Langetepe, David Kübel
2016 arXiv   pre-print
For a class of environments (convex shapes and shapes with kernel positions), we design an online strategy that always leaves the environment.  ...  Due to the additional information, the certificate path always (for any position s) leaves the environment earlier than the ultimate escape path, in the above convex examples.  ...  Acknowledgements: We would like to thank all anonymous referees for their helpful comments and suggestions.  ... 
arXiv:1604.05972v1 fatcat:7xgiwjevy5gzxl5i3wcmrrgyie

Page 7913 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Summary: “The online kernel-search problem is for a mobile robot with 360° vision to move from a starting point to the closest kernel point within an unknown star-shaped polygon.  ...  The codes for segment/ray-segment intersection, segment/ray-triangle intersection, for point in polyhedron, and for computing a De- launey triangulation from the three-dimensional convex hull are four  ... 

On the Optimality of Spiral Search [chapter]

Elmar Langetepe
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
Searching for a point in the plane is a well-known search game problem introduced in the early eighties.  ...  The best known search strategy is given by a spiral and achieves a competitive ratio of 17.289 . . .  ...  Acknowledgements: The author would like to thank the anonymous referees for their valuable comments for improving the paper.  ... 
doi:10.1137/1.9781611973075.1 dblp:conf/soda/Langetepe10 fatcat:mh4suknrfbbclmhiyuiwme7ma4

Optimal competitive online ray search with an error-prone robot [article]

Tom Kamphans, Elmar Langetepe
2010 arXiv   pre-print
We consider the problem of finding a door along a wall with a blind robot that neither knows the distance to the door nor the direction towards of the door.  ...  We study the case that the robot's movement is erroneous. In this case the doubling strategy is no longer optimal.  ...  Both approaches lead to the so called doubling strategy, which is a basic paradigma for searching algorithms, e. g. searching for a point on m rays, see [7] , or approximating the optimal search path,  ... 
arXiv:1012.5259v1 fatcat:vzbhapko3jhi3kathz5arexlym

Competition of Charge-Density Waves and Superconductivity in Sulfur

O. Degtyareva, M. V. Magnitskaya, J. Kohanoff, G. Profeta, S. Scandolo, M. Hanfland, M. I. McMahon, E. Gregoryanz
2007 Physical Review Letters  
A one-dimensional charge-density wave (CDW) instability is shown to be responsible for the formation of the incommensurate modulation of the atomic lattice in the high-pressure phase of sulfur.  ...  , the same phenomenology found in doped layered dichalcogenides.  ...  area for searching for a CDW state.  ... 
doi:10.1103/physrevlett.99.155505 pmid:17995182 fatcat:trszkg5qvvh5pcf7rwjowczj7y

Globally Consistent Multi-label Assignment on the Ray Space of 4D Light Fields

Sven Wanner, Christoph Straehle, Bastian Goldluecke
2013 2013 IEEE Conference on Computer Vision and Pattern Recognition  
We present the first variational framework for multi-label segmentation on the ray space of 4D light fields.  ...  As a further contribution, we make all light fields available online with complete depth and segmentation ground truth data where available, and thus establish the first benchmark data set for light field  ...  Ray space A 4D light field or Lumigraph is defined on a ray space R, the set of rays passing through two planes Π and Ω in R 3 , where each ray can be uniquely identified by its two intersection points  ... 
doi:10.1109/cvpr.2013.135 dblp:conf/cvpr/WannerSG13 fatcat:g5gklntkxjbsllt64ceei5eymi

Improvement of contact-less KID design using multilayered Al/Ti material for resonator [article]

J. Colas, M. Calvo, J. Goupy, A. Monfardini, M. De Jesus, J. Billard, A. Juillard, L. Vagneron
2021 arXiv   pre-print
The necessity to increase exposure in rare event searches experiments by maintaining a low energy threshold and a good energy resolution leads to segmented detectors as in EDELWEISS (Dark Matter), CUORE  ...  Using a 30 g silicon target absorber with Al/Ti multilayers for the KID resonator, we report a significant improvement of our detector response exhibiting a keV-scale energy resolution combined with the  ...  Acknowledgements This work is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program under Grant Agreement ERC-StG-CENNS 803079  ... 
arXiv:2111.12857v1 fatcat:63vs3xycpbd7td2zq6fo4wviiq

Pressure tuning of competing magnetic interactions in intermetallic CeFe2

Jiyang Wang, Yejun Feng, R. Jaramillo, Jasper van Wezel, P. C. Canfield, T. F. Rosenbaum
2012 Physical Review B  
CeFe_2 is a geometrically frustrated ferromagnet that lies close to an instability at which a subtle change in the lattice symmetry couples to a transition to antiferromagnetism.  ...  We use x-ray diffraction, diamond-anvil-cell techniques, and numerical simulation to identify the ground states and to quantitatively illustrate effects of competing magnetic energy scales and geometrical  ...  Acknowledgments The work at the University of Chicago was supported  ... 
doi:10.1103/physrevb.86.014422 fatcat:plycik7t5zes3byfho3lz5ealq
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