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On the parallel-decomposability of geometric problems

Mikhail J. Atallah, Jyh -Jong Tsay
1992 Algorithmica  
There is a large and growing body of literature concerning the solutions of geometric problems on mesh-connected arrays of processors.  ...  Most of these algorithms are optimal (i.e. tun in time D(n l / d ) on a d-dimensiona.l a-processor array), and they all assume that the parallel machine is trying to solve a problem of size n on an n-processor  ...  On the other hand, the time to decompose the computation into subcomputations and to schedule the subcomputations must be counted in the study of the parallel-decomposability (Le., it has to be of O(Seq  ... 
doi:10.1007/bf01758844 fatcat:ktr4mztewvbdtiic32yxewhp54

On the parallel decomposability of geometric problems

M. J. Atallah, J. J. Tsay
1989 Proceedings of the fifth annual symposium on Computational geometry - SCG '89  
There is a large and growing body of literature concerning the solutions of geometric problems on mesh-connected arrays of processors.  ...  Most of these algorithms are optimal (i.e. tun in time D(n l / d ) on a d-dimensiona.l a-processor array), and they all assume that the parallel machine is trying to solve a problem of size n on an n-processor  ...  On the other hand, the time to decompose the computation into subcomputations and to schedule the subcomputations must be counted in the study of the parallel-decomposability (Le., it has to be of O(Seq  ... 
doi:10.1145/73833.73845 dblp:conf/compgeom/AtallahT89 fatcat:ozen5wx2ebajdox625xln372ie

Domain Decomposition Methods for Parallel Laser-Tissue Models with Monte Carlo Transport [chapter]

Henry J. Alme, Garry Rodrigue, George Zimmerman
2000 Monte-Carlo and Quasi-Monte Carlo Methods 1998  
We will present speedup and load balance results obtained for a suite of problems decomposed using a few domain decomposition algorithms we have developed. ?  ...  to simulate the conduction of the temperature field in the tissue.  ...  Acknowledgment The authors wish to thank X Division and the Institute for Scientific Computing Research (ISCR) at the Lawrence Livermore National Laboratory for their support in this research.  ... 
doi:10.1007/978-3-642-59657-5_8 fatcat:5vvbbk25dzf2blmsisjcxp7cjm

Task Decomposition Using Geometric Relation for Min-Max Modular SVMs [chapter]

Kaian Wang, Hai Zhao, Baoliang Lu
2005 Lecture Notes in Computer Science  
In this paper, we explore the use of the geometric relation among training data in task decomposition.  ...  M 3 -SVM divides training data to several sub-sets, and combine them to a series of independent sub-problems, which can be learned in a parallel way.  ...  The original problems are decomposed according to the parameters shown in Table 1 and Table 2 . Table 3 presents simulation results on Forest CoverType problem.  ... 
doi:10.1007/11427391_142 fatcat:562a4dp5sbbbhik5l5vz5cm5sm

Parallel (‖) ELLPACK: an expert system for parallel processing of partial differential equations

E.N. Houstis, J.R. Rice, T.S. Papatheodorou
1989 Mathematics and Computers in Simulation  
In order to support the solution of elliptic PDEs on fixed meshes, we are building a library of finite difference and element discretization methods and direct/iterative solvers for the NCUBE and SEQUENT  ...  Ahstract We are developing an expen system environment for solving elliptic partial differential equations(pDEs) defined on two and three dimensional domains on MIMD type parallel machines.  ...  We are also exploring the alternative of decomposing the domain directly in geometric tenns.  ... 
doi:10.1016/0378-4754(89)90143-2 fatcat:vgbqwicvangmjknom3wvpcsvwa

Embarrassingly Parallel Search [chapter]

Jean-Charles Régin, Mohamed Rezgui, Arnaud Malapert
2013 Lecture Notes in Computer Science  
Thanks to it, a user can parallelize the resolution of its problem without modifying the solver or writing any parallel source code and can easily replay the resolution of a problem.  ...  The experiments on satisfaction problems and on optimization problems suggest that generating between thirty and one hundred subproblems per worker leads to a good scalability.  ...  We would like to thank very much Laurent Perron and Claude Michel for their comments which helped improve the paper.  ... 
doi:10.1007/978-3-642-40627-0_45 fatcat:xgnox4f6qrg7hmj4g2pia2pgli

Spatial geometric constraint solving based on k-connected graph decomposition

Gui-Fang Zhang, Xiao-Shan Gao
2006 Proceedings of the 2006 ACM symposium on Applied computing - SAC '06  
Based on this analysis, problems similar to the "double banana problem" could be easily detected.  ...  We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones if possible.  ...  This paper will focus on using graph algorithms to decompose a large constraint problem into smaller ones. In [11] , Owen proposed a GCS method based on the triconnected decomposition of graphs.  ... 
doi:10.1145/1141277.1141510 dblp:conf/sac/ZhangG06 fatcat:o4zj4qaso5fcxhs2mcextj5224

Tree-decomposable and Underconstrained Geometric Constraint Problems [article]

Ioannis Fudos, Christoph M. Hoffmann, Robert Joan-Arinyo
2017 arXiv   pre-print
In this paper, we are concerned with geometric constraint solvers, i.e., with programs that find one or more solutions of a geometric constraint problem.  ...  Owing to the complexity, type or difficulty of a constraint problem, it is possible that the solver does not find a solution even though one may exist.  ...  Acknowledgement Hoffmann gratefully acknowledges partial support by the National Science Foundation under award 1361783.  ... 
arXiv:1608.05205v3 fatcat:eoepj4luvfa23h4g4vmii3es34

Geometric Constraint Solving Based on Connectivity of Graph

Gui-Fang Zhang, Xiao-Shan Gao
2004 Computer-Aided Design and Applications  
We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones if possible.  ...  The method works in both 2D and 3D cases. We also show how to merge two rigid bodies if they share two or three geometric primitives in a bi-connected or tri-connected graph respectively.  ...  This paper will focus on using graph algorithms to decompose a large constraint problem into smaller ones.  ... 
doi:10.1080/16864360.2004.10738289 fatcat:6bgqzfzhvjht3fxbzjhmzuztle

Parallel techniques for computational geometry

M.J. Atallah
1992 Proceedings of the IEEE  
Since the focus is on general algorithmic techniques rather than on specific problems, no attempt is made to list all of the known parallel complexity bounds for geometric problems (there are too many  ...  Section 2 briefly reviews parallel models, Section 3 discusses basic subproblems that tend to arise in the solution of geometric problems on any parallel model, Section 4 discusses PRAM techniques, Section  ...  It is a pleasure to acknowledge the helpful comments of Danny Chen on a earlier draft of this survey.  ... 
doi:10.1109/5.163410 fatcat:g3ipxiqhhjgbrmquka2rywtbd4

Geometric constraint solving: The witness configuration method

Dominique Michelucci, Sebti Foufou
2006 Computer-Aided Design  
Solvers use numerical resolution for big irreducible constraints systems, and formulas for small problems, e.g., computing the length of the third side of a triangle knowing one angle and the two other  ...  Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution.  ...  Conclusion This paper proposed a new strategy for studying and decomposing systems of geometric constraints.  ... 
doi:10.1016/j.cad.2006.01.005 fatcat:zhf2xdvhnrbq3f37q6zmb7rfi4

A shortest path algorithm for a nonrotating object among obstacles of arbitrary shapes

P.L. Lin, Shyang Chang
1993 IEEE Transactions on Systems, Man and Cybernetics  
In addition, a simple geometric algorithm is proposed to check the existence of safe paths between the given initial and final positions.  ...  A shortest path algorithm for motion planning problem via mathematical morphology is proposed. The moving object and obstacles can be of arbitrary shapes of finite size.  ...  Based on this observation, the 2-D shortest path problem can be immediately reduced to the problem of a discrete graph search and solved in polynomial time.  ... 
doi:10.1109/21.256552 fatcat:ykrqolkqbzfovlh2puawogiyuq

Single-Image 3D Pose Estimation for Texture-Less Object via Symmetric Prior

Xiaoyuan REN, Libing JIANG, Xiaoan TANG, Junda ZHANG
2018 IEICE transactions on information and systems  
Firstly, by parameterized representation, the texture-less object is decomposed into a series of subobjects with regular geometric primitives.  ...  The effectiveness of the proposed method is verified by the experiments based on simulated and measured data.  ...  One is structural symmetry of sub-objects, each of which is represented as parameterized regular geometric primitive.  ... 
doi:10.1587/transinf.2018edl8014 fatcat:zi4zphyhyre4fhja6sscdmgo7a

A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially-Tailored Local Coordinate System

Haiyan Yu, Yuanjun He, Wenjun Zhang
2021 IEEE Access  
Among them, one example is related to the robustness of methods for analyzing the relations of two interacting objects, which is still an open issue in the field of geometric computing and suggests that  ...  Conventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems.  ...  the original geometric problem.  ... 
doi:10.1109/access.2021.3074509 fatcat:xp4unmpaofd7dnjhygpnkqrmcq

Component-level parallelization of triangular decompositions

Marc Moreno Maza, Yuzhen Xie
2007 Proceedings of the 2007 international workshop on Parallel symbolic computation - PASCO '07  
geometric objects, * medium/fine grained level for polynomial arithmetic within each task. to develop a solver for which the number of processes in use depends on the geometry of the solution set 8 Ideally  ...  between Manager and Worker's is controlled by a mailbox protocol. • Tests on 7 well-known problems: -Sequential runs with and without regularized initials -Parallel with Task Pool Dimension and Rank Guided  ...  All the examples but one are zero-dimensional (= finite number of solutions): a situation where redundant components are very rare.  ... 
doi:10.1145/1278177.1278189 dblp:conf/issac/MazaX07 fatcat:crlw5qddpvcgplyw5mst532nha
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