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Random-Edge Is Slower Than Random-Facet on Abstract Cubes

Thomas Dueholm Hansen, Uri Zwick, Thomas Hansen
The behavior of Random-Edge is much less understood. We show that in the AUSO setting, Random-Edge is slower than Random-Facet.  ...  Random-Edge and Random-Facet are two very natural randomized pivoting rules for the simplex algorithm. The behavior of Random-Facet is fairly well understood.  ...  I C A L P 2 0 1 6 51:8 Random-Edge Is Slower Than Random-Facet on Abstract Cubes Proof.  ... 

Errata for: A subexponential lower bound for the Random Facet algorithm for Parity Games [article]

Oliver Friedmann and Thomas Dueholm Hansen and Uri Zwick
2014 arXiv   pre-print
number of pivoting steps performed by Random-Facet^*, a variant of Random-Facet that bases its random decisions on one random permutation.  ...  Unfortunately, the claim that the expected numbers of steps performed by Random-Facet and Random-Facet^* are the same is false.  ...  The Random-Facet * algorithm is identical to the Random-Facet algorithm, except that it takes as an additional argument a permutation σ : E → {1, . . . , |E|} of the edges and always removes the first  ... 
arXiv:1410.7871v1 fatcat:dlj3nlyqwjfmlodj7ffpgxnpaq

Improved upper bounds for Random-Edge and Random-Jump on abstract cubes [chapter]

Thomas Dueholm Hansen, Mike Paterson, Uri Zwick
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
For Random-Edge, we obtain an upper bound of about 1.80 n , improving upon the the previous upper bound of about 2 n /n log n obtained by Gärtner and Kaibel.  ...  AUSOs provide an appealing combinatorial abstraction of linear programming and other computational problems such as finding optimal strategies for turn-based Stochastic Games.  ...  Is Random-Edge faster or slower than Random-Facet?  ... 
doi:10.1137/1.9781611973402.65 dblp:conf/soda/HansenPZ14 fatcat:vfzwhn62xbgjvgfrtgl3ttr6qy

Dynamic Minkowski sum of convex shapes

Evan Behar, Jyh-Ming Lien
2011 2011 IEEE International Conference on Robotics and Automation  
We show that DYMSUM is significantly more efficient than the traditional approach, in particular when the size of the input polyhedra are large and when the rotation is small between frames.  ...  More steps per 2π means slower rotational speed. Fig. 5 . 5 Computation times of DYMSUM and brute force of two identical cubes.  ...  We use a 10×10× 10 cube with different numbers of triangles tessellated on the surface.  ... 
doi:10.1109/icra.2011.5979992 dblp:conf/icra/BeharL11 fatcat:jsl6wfxdsrfynnksdgyaewkbda

There are 174 Subdivisions of the Hexahedron into Tetrahedra [article]

Jeanne Pellerin and Kilian Verhetsel and Jean-Francois Remacle
2018 arXiv   pre-print
It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra.  ...  However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions.  ...  ACKNOWLEDGMENTS is research is supported by the European Research Council (project HEXTREME, ERC-2015-AdG-694020).  ... 
arXiv:1801.01288v2 fatcat:jcg2at3zmvcx3p4xp6eiadubtu

Pseudo Unique Sink Orientations [article]

Vitor Bosshard, Bernd Gärtner
2017 arXiv   pre-print
We show that PUSOs have a much more rigid structure than USOs and that their number is between 2^Ω(2^n- n) and 2^O(2^n) which is negligible compared to the number of USOs.  ...  A unique sink orientation (USO) is an orientation of the n-dimensional cube graph (n-cube) such that every face (subcube) has a unique sink. The number of unique sink orientations is n^Θ(2^n).  ...  It is unknown which of the two algorithms is better on actual LPs, but on AUSOs, RandomEdge is strictly slower in the worst case [9] .  ... 
arXiv:1704.08481v1 fatcat:y6dzm3xgijbbzlroqnx2esgkdy

Exponential lower bounds for history-based simplex pivot rules on abstract cubes [article]

Antonis Thomas
2017 arXiv   pre-print
We give exponential lower bounds on Acyclic Unique Sink Orientations (AUSO) of the abstract cube, for all of these pivot rules.  ...  For Johnson's rule our bound is the first superpolynomial one in any context; for Zadeh's it is the first one for AUSO. Those two are our main results.  ...  Random-edge is slower than random-facet on abstract cubes. In ICALP 2016, pages 51:1–51:14, 2016. doi:10.4230/ LIPIcs.ICALP.2016.51. [16] G. Kalai.  ... 
arXiv:1706.09380v1 fatcat:zbywu54365arphdrk7acyismoa

Simple and Efficient Distribution-Sensitive Point Location in Triangulations [chapter]

Pedro Machado Manhães de Castro, Olivier Devillers
2011 2011 Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
For a batch of query points, the main idea is to use previous queries to improve the current one.  ...  We analyze, implement, and evaluate a distributionsensitive point location algorithm based on the classical Jump & Walk, called Keep, Jump, & Walk.  ...  When the cube edge size is bigger than 0.01, then Figure 9-bottom shows a rapidly degradation of the last-point strategy performance; the last-point strategy should not be used when there is no a priori  ... 
doi:10.1137/1.9781611972917.13 dblp:conf/alenex/CastroD11 fatcat:niq25yysznh2fd7zvnwsh543i4

Polyhedral voronoi diagrams for additive manufacturing

Jonàs Martínez, Samuel Hornus, Haichuan Song, Sylvain Lefebvre
2018 ACM Transactions on Graphics  
The stochastic geometry has an impact on printing speed (about 15% slower than straight line infill on our printers).  ...  Each bisector vertex is generated by either an edge-edge pair or a vertex-facet pair (see Figure 6 ). Details are given in the supplemental material.  ... 
doi:10.1145/3197517.3201343 fatcat:yztd2tuzevhmdivzyk7wig766i

Detecting the intersection of two convex shapes by searching on the 2-sphere

Samuel Hornus
2017 Computer-Aided Design  
We provide an in-depth geometrical understanding of the differences between GJK and our technique and conclude that our technique is probably a good drop-in replacement when one is not interested in the  ...  We describe a new technique that works explicitly on the unit sphere, interpreted as the sphere of directions.  ...  The three edge half-lengths are uniformly random in [0, 1], the center of each box is uniformly random in a zerocentered cube of side length σ and the box is randomly oriented.  ... 
doi:10.1016/j.cad.2017.05.009 fatcat:oawm643e2rdhdnoykk4sznoqg4

3D cellular automata simulations of intra and intergranular corrosion

D. di Caprio, J. Stafiej, G. Luciano, L. Arurault
2016 Corrosion Science  
ARTICLE INFO ABSTRACT A simple mode! for the effect of intergranular corrosion on overall corrosion processes is investigated using a cellular automata approach.  ...  The corrosion probability for grain boundary is set to a value higher than it is for the grain core.  ...  The first case, referred to as cube piling (CP), is a regular piling with cubes one above the other with matching edges.  ... 
doi:10.1016/j.corsci.2016.07.028 fatcat:q4am4abkajbgzef23ntjmwu4em

Boolean operations on 3D selective Nef complexes: Data structure, algorithms, optimized implementation and experiments

Peter Hachenberger, Lutz Kettner, Kurt Mehlhorn
2007 Computational geometry  
ACIS is mostly faster, by a factor up to six. There are examples on which ACIS fails.  ...  Nef in his seminal 1978 book on polyhedra. The generality of Nef complexes is essential for some applications.  ...  Acknowledgements We thank Michael Seel and Susan Hert for their work on planar Nef polyhedra and their initial parts for the 3D implementation.  ... 
doi:10.1016/j.comgeo.2006.11.009 fatcat:n5jkuqyhkzeyvlcl6him3cdqo4

The Effects of Representation and Juxtaposition on Graphical Perception of Matrix Visualization

Xiaotong Liu, Han-Wei Shen
2015 Proceedings of the 33rd Annual ACM Conference on Human Factors in Computing Systems - CHI '15  
Analyzing multiple networks at once is a common yet difficult task in many domains.  ...  We investigate the effects of using square matrices and triangular matrices on the speed and accuracy of performing graphical-perception tasks.  ...  INTRODUCTION A network is an abstract data type that represents entities as nodes and their relationships as edges.  ... 
doi:10.1145/2702123.2702217 dblp:conf/chi/LiuS15 fatcat:cetfmehutbcznk7v7witsc7p6a

Hopper flow of irregularly shaped particles (non-convex polyhedra): GPU-based DEM simulation and experimental validation

Nicolin Govender, Daniel N. Wilke, Chuan-Yu Wu, Johannes Khinast, Patrick Pizette, Wenjie Xu
2018 Chemical Engineering Science  
To that end, the most flexible approach to capture the particle shape is via a polyhedron, which provides a faceted representation of any shape, albeit at a significant computational cost.  ...  Capturing the particle non-convexity is important since it allows to model the physical interlocking when the particles are in contact.  ...  The financial support of the National Research Foundation (NRF) of South Africa is acknowledged.  ... 
doi:10.1016/j.ces.2018.05.011 fatcat:ezhsroioxfgm3mkhzfce6g3yle


Clément Jamin, Pierre Alliez, Mariette Yvinec, Jean-Daniel Boissonnat
2015 ACM Transactions on Mathematical Software  
Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input  ...  CGALmesh provides guarantees on approximation quality as well as on the size and shape of the mesh elements.  ...  Given an input surface S, the medial axis of S is defined as the locus of points that have more than one closest point on S.  ... 
doi:10.1145/2699463 fatcat:eqp4lzfhabgppg24zb3fwy447u
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