On Parallel Methods of Multibody Dynamics

2003 ◽  
Author(s):  
James H. Critchley ◽  
Kurt S. Anderson
Keyword(s):  
Time Complexity ◽  
Multibody System ◽  
Practical Importance ◽  
Divide And Conquer ◽  
Optimal Time ◽  
Worst Case ◽  
Parallel Methods ◽  
Divide And Conquer Algorithm ◽  
Coordinate Reduction ◽  
Parallel Arrays

Optimal time efficient parallel computation methods for large multibody system dynamics are defined and investigated in detail. Comparative observations are made which demonstrate significant deficiencies in operating regions of practical importance and a new parallel algorithm is generated to address them. The new method of Recursive Coordinate Reduction Parallelism (RCRP) outperforms or directly reduces to the fastest general multibody algorithms available for small parallel resources and obtains “O(logk(n))” time complexity in the presence of larger parallel arrays. Performance of this method relative to the Divide and Conquer Algorithm is illustrated with an operations count for the worst case of a multibody chain system.

An Efficient Multibody Divide and Conquer Algorithm

2005 ◽  
Author(s):  
James H. Critchley
Keyword(s):  
Multibody Dynamics ◽  
Time Complexity ◽  
Future Generation ◽  
Parallel Computers ◽  
Parallel Processors ◽  
Divide And Conquer ◽  
Parallel Computer ◽  
Divide And Conquer Algorithm ◽  
Computer Resources ◽  
Theoretical Minimum

A new and efficient form of Featherstone’s multibody Divide and Conquer Algorithm (DCA) is presented. The DCA was the first algorithm to achieve theoretically optimal logarithmic time complexity with a theoretical minimum of parallel computer resources for general problems of multibody dynamics, however the DCA is extremely inefficient in the presence of small to modest parallel computers. The new efficient DCA approach (DCAe) demonstrates that large DCA subsystems can be constructed using fast sequential techniques and realize substantial speed increases in the presence of as few as two parallel processors. Previously the DCA was a tool intended for a future generation of parallel computers, this enhanced version promises practical and competitive performance with the parallel computers of today.

Distributed Operational Space Formulation of Serial Manipulators

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
James Critchley ◽  
Denny Oetomo ◽  
Roy Featherstone ◽  
Oussama Khatib
Keyword(s):  
Parallel Algorithms ◽  
Time Complexity ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Divide And Conquer ◽  
Serial Manipulators ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Space Formulation ◽  
Space Dynamics

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

An Efficient Multibody Divide and Conquer Algorithm and Implementation

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
James H. Critchley ◽  
Kurt S. Anderson ◽  
Adarsh Binani
Keyword(s):  
Multibody Dynamics ◽  
Time Complexity ◽  
Future Generation ◽  
Parallel Computers ◽  
Divide And Conquer ◽  
Parallel Computer ◽  
Recursive Method ◽  
Divide And Conquer Algorithm ◽  
Computer Resources ◽  
Theoretical Minimum

A new and efficient form of Featherstone’s multibody divide and conquer algorithm (DCA) is presented and evaluated. The DCA was the first algorithm to achieve theoretically the optimal logarithmic time complexity with a theoretical minimum of parallel computer resources for general problems of multibody dynamics; however, the DCA is extremely inefficient in the presence of small to modest parallel computers. This alternative efficient DCA (DCAe) approach demonstrates that large DCA subsystems can be constructed using fast sequential techniques to realize a substantial increase in speed. The usefulness of the DCAe is directly demonstrated in an application to a four processor workstation and compared with the results from the original DCA and a fast sequential recursive method. Previously the DCA was a tool intended for a future generation of parallel computers; this enhanced version delivers practical and competitive performance with the parallel computers of today.

Design and Implementation of an Efficient Multibody Divide and Conquer Algorithm

2007 ◽  
Author(s):  
James H. Critchley ◽  
Adarsh Binani ◽  
Kurt Anderson
Keyword(s):  
Time Complexity ◽  
Future Generation ◽  
Parallel Computers ◽  
Divide And Conquer ◽  
Parallel Computer ◽  
Recursive Method ◽  
Design And Implementation ◽  
Divide And Conquer Algorithm ◽  
Computer Resources ◽  
Theoretical Minimum

A new and efficient form of Featherstone’s multibody Divide and Conquer Algorithm (DCA) is presented. The DCA was the first algorithm to achieve theoretically optimal logarithmic time complexity with a theoretical minimum of parallel computer resources for general problems of multibody dynamics, however the DCA is extremely inefficient in the presence of small to modest parallel computers. This alternative efficient DCA approach (DCAe) demonstrates that large DCA subsystems can be constructed using fast sequential techniques to realize a substantial increase in speed. The usefullness of the DCAe is directly demonstrated in an application to a four processor workstation and compared with results from the original DCA and a fast sequential recursive method. Previously the DCA was a tool intended for a future generation of parallel computers, this enhanced version delivers practical and competitive performance with the parallel computers of today.

New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Imad M. Khan ◽  
Mohammad Poursina
Keyword(s):  
Multibody Dynamics ◽  
Large Deformations ◽  
Multibody System ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Ongoing Research ◽  
Flexible Bodies ◽  
Computational Burden ◽  
Divide And Conquer Algorithm ◽  
Model Fidelity

This work presents a survey of the current and ongoing research by the authors who use the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with various aspects of multibody dynamics. This work provides a brief discussion of various topics that are extensions of previous DCA-based algorithms or novel uses of this algorithm in the multibody dynamics context. These topics include constraint error stabilization, spline-based modeling of flexible bodies, model fidelity transitions for flexible-body systems, and large deformations of flexible bodies. It is assumed that the reader is familiar with the “Advances in the Application of the DCA to Multibody System Dynamics” text as the notation used in this work is explained therein and provides a summary of how the DCA has been used previously.

Constructing Delaunay Triangulations by Merging Buckets in Quad Tree Order

1988 ◽  
Vol 11 (3) ◽  
pp. 275-288
Author(s):  
Jyrki Katajainen ◽  
Markku Koppinen
Keyword(s):  
Delaunay Triangulation ◽  
Slight Modification ◽  
Divide And Conquer ◽  
Worst Case ◽  
Delaunay Triangulations ◽  
Running Time ◽  
Expected Time ◽  
Divide And Conquer Algorithm ◽  
Quad Tree ◽  
Average Running Time

Recently Rex Dwyer [D87] presented an algorithm which constructs a Delaunay triangulation for a planar set of N sites in O(N log log N) expected time and O(N log N) worst-case time. We show that a slight modification of his algorithm preserves the worst-case running time, but has only O(N) average running time. The methcxl is a hybrid which combines the cell technique with the divide-and-conquer algorithm of Guibas & Stolfi [GS85]. First a square grid of size about N by N is placed on the set of sites. The grid forms about N cells (buckets), each of which is implemented as a list of the sites which fall into the corresponding square of the grid. A Delaunay triangulation of the generally rather few sites within each cell is constructed with the Guibas & Stolfi algorithm. Then the triangulations are merged, four by four, in a quadtree-like order.

scholarly journals Rotation Algorithms for Balancing Search Trees

1970 ◽  
Vol 10 (1) ◽  
pp. 26-32
Author(s):  
Chumphol Bunkhumpornpat ◽  
Varin Chouvatut ◽  
Saowaluk Rattanaudomsawat
Keyword(s):  
Data Structure ◽  
Hierarchical Structure ◽  
Time Complexity ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Search Tree ◽  
Optimal Time ◽  
Worst Case ◽  
Cluster Membership ◽  
The Hierarchical Structure

A search tree is a data structure constructed from a minimum spanning tree. This data structure is used for determining the cluster membership of a query instance clustered by a similarity-guaranteed clustering algorithm. According to the line topology of a search tree in the worst case, the time complexity of tree traversing is O(n) where n is the number of nodes of the tree. Unfortunately, the AVL tree algorithm cannot solve this problem because the algorithm is unable to maintain the hierarchical structure of a search tree. From the definition of balance factor, our proposed algorithm is designed to rotate nodes until the tree becomes balanced while maintaining the hierarchical structure. Consequently, the balanced search tree achieves the optimal time complexity of O(log n) for the searching purpose.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

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