Download or read book A parallel algorithm for constructing minimum spanning trees written by Carnegie-Mellon University. Computer Science Dept and published by . This book was released on 1979 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Linear work Parallel Algorithm for Finding Minimum Spanning Trees written by Princeton University. Dept. of Computer Science and published by . This book was released on 1994 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We give the first linear-work parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2[superscript log*n]log n) expected time. It is a modification of the sequential linear-time algorithm of Klein and Tarjan."
Download or read book Two Papers on a Tree Structured Parallel Computer written by Jon Louis Bentley and published by . This book was released on 1979 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report consists of two papers describing various aspects of a new tree-structured parallel computer. The first paper, 'A tree machine for searching problems' by J.L. Bentley and H.T. Kung, describes the basic architecture of the machine. A set of N elements can be maintained on an N-processor version of the machine such that insertions, deletions, queries and updates can all be processed in 2 lg N time units. The queries can be very complex, including problems arising in ordered set manipulation, data bases, and statistics. The machine is pipelined so that M successive operations can be performed in M-1 + 2 lg N time units. The paper studies both the basic machine structure and a VLSI implementation of the machine. The second paper, 'A parallel algorithm for constructing minimum spanning trees' by J.L. Bentley, shows how an (N/lg N)-processor version of the machine can solve the problem of constructing minimum spanning trees in time proportional to N lg N. This algorithm is an improvement over existing algorithms in several ways. (Author).
Download or read book Parallel Update of Minimum Spanning Trees in Logarithmic Time written by I. V. Ramakrishnan and published by . This book was released on 1984 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel algorithms are presented for updating a minimum spanning tree when the cost of an edge changes or when a new node is inserted in the underlying graph. The machine model used is a parallel random access machine which allows simultaneous reads but prohibits simultaneous writes into the same memory location. The algorithms described in this paper for updating a minimum spanning tree require O(log n) time and O(n square) processors. These algorithms are efficient when compared to previously known algorithms for initial construction of a minimum spanning tree that require O(log n to the base 2) time and use O(n square) processors.
Download or read book An Adaptive and Cost optimal Parallel Algorithm for Minimum Spanning Trees written by Selim G. Akl and published by . This book was released on 1984 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Synchronous Parallel Algorithm for the Minimum Spanning Tree Problems written by Tapan K. Mallik and published by . This book was released on 1986 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Implementation of Bor vka s Minimum Spanning Tree Algorithm written by Sun Chung and published by . This book was released on 1996 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We study parallel algorithms for the minimum spanning tree problem, based on the sequential algorithm of Borůvka. The target architectures for our algorithm are asynchronous, distributed-memory machines. Analysis of our parallel algorithm, on a simple model that is reminiscent of the LogP model, shows that in principle a speedup proportional to the number of processors can be achieved, but that communication costs can be significant. To reduce these costs, we develop a new randomized linear work pointer jumping scheme that performs better than previous linear work algorithms. We also consider empirically the effects of data imbalance on the running time. For the graphs used in our experiments, load balancing schemes result in little improvement in running times. Our implementations on sparse graphs with 64,000 vertices on Thinking Machine's CM-5 achieve a speedup factor of about 4 on 16 processors. On this environment, packaging of messages turns out to be the most effective way to reduce communication costs."
Download or read book A Nearly Optimal Parallel Algorithm for Constructing Depth First Spanning Trees in Planar Graphs written by Xin He and published by . This book was released on 1987 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simple Parallel Algorithms for the Replacement Edge Problem and Related Problems on Minimum Spanning Trees written by Jyrki Katajainen and published by . This book was released on 1994 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Let G be a connected, undirected, weighted graph with n vertices and m edges. Further, let S be a spanning tree of G and T and a minimum spanning tree of G. We present parallel algorithms for the following problems: (a) Given G and T, determine, for each edge e of T, a non-tree edge f by which e should be replaced to create a new minimum spanning tree if e is removed from G. (b) Given G, determine a most vital edge of G (with respect to minimum spanning trees), that is, an edge whose removal from G has the largest impact on the weight of a minimum spanning tree of the remaining graph. (c) Given G and S, determine whether S is a minimum spanning tree of G. (d) Given G and T, compute, for each edge e of G, by how much the weight of e can change without affecting the minimality of T. The algorithms run in O(log n) time and O(m) space with m processors. The problems (a), (b), and (d) are solved on a MINIMUM CRCW PRAM, whereas the problem (c) is solved on a CREW PRAM. The algorithms utilize a simple technique for computing functions defined on paths in trees that might be of independent interest."
Download or read book Boruvka Minimum Spanning Tree Parallel Algorithm with Applications to Satellite Networks written by Colby D. LaRue and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimum Spanning Tree (MST) algorithms are used in many fields. This thesis will start by walking through various classical algorithms for finding a minimum spanning tree for a graph and weighing the pros and cons of each algorithm for different types of graphs, such as complete, large, or disconnected graphs. Then, Boruvka’s MST algorithm will be reviewed in greater detail. One of the major issues with most graph algorithms is that they can be slow for large data sets due to the serial nature of classical algorithms, and for many applications, this is acceptable. However, if an application needs to perform this calculation in a matter of seconds, it is not likely to be performant. Consider the use case of a large moving satellite constellation that must continuously find its most optimal network topology. With the rise of ubiquitous computing and the Internet of Things, the efficiency of algorithms is as vital as ever, with applications ranging from agriculture and defense to medical research and finance. Even digital art has applications with the development of new artificial intelligence and machine learning algorithms. This study will focus on a space research application involving prominent moving satellite constellations. There are many techniques to improve existing algorithms. Considering a parallel implementation is often essential when scalability or performance is a concern. Precisely for this study, parallelization of the minimum spanning tree algorithm is considered. After reviewing the techniques used for parallelizing algorithms, a parallel implementation of Boruvka’s algorithm will be written based on the contractive approach. A time complexity analysis of the serial Boruvka algorithm will then be compared to the parallelized version of Boruvka’s algorithm. While graph algorithms for supercomputers, high-performance computers, and GPUs have been studied extensively, few results exist for the emerging multi-core CPU platforms. Our work is addressing one of the fundamental problems in graph theory and applications, the calculation of the MST for a given graph. Multiple algorithms for calculating the MST exist. We are reporting here on our implementation of Boruvka’s MST algorithm that runs either serially on one CPU core, or in parallel on two or more cores. We report the efficiency gains made when applying our implementation of the algorithm to large random graphs, with increasing the number of cores. We then quantify its performance on a real-world graph that represents a large satellite network. An example satellite constellation will be used based on SpaceX’s Starlink commercial constellation. The results will be compared using one instance in time of the constellation. This application of the spanning tree can be easily integrated with a real time simulation framework. This thesis will outline a basic example of how that might be done using the CesiumJS library. The parallelized Boruvka minimum spanning tree implementation was run with various data sets and compared to the classical algorithm implementation. The speedup was on the order of approximately 10% with 8 goroutines.
Download or read book Parallel Implementation of a Minimum Spanning Tree Algorithm written by Jarim Seo and published by . This book was released on 2020 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building a Minimum Spanning Tree (MST) of a weighted undirected graph is an important step in various applications, including circuit design, and it is desirable to build the MST quickly. However, current well-known approaches for building MSTs are not highly parallel. In this thesis, I propose a new algorithm to build MSTs in parallel. My new algorithm can be divided into two main steps: adding the ‘obvious edges’ of the MST and connecting the components produced by the first step. I parallelized both steps using various atomic operations. Two serial and two parallel MST implementations were used for performance comparisons. Based on the geometric mean over 14 graphs, my MST implementation is faster than the Edge Pruning MST approach but slower than Boost. Moreover, when run in parallel with 16 threads, my code is slower than both Galois and the Problem Based Benchmark Suite implementation.
Download or read book Parallel Algorithms for the Minimum Spanning Tree Problem written by Narsingh Deo and published by . This book was released on 1981 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Parallel Algorithm of Constructing a Voronoi Diagram on Hypercube Connected Computer Networks written by Wenmao Chai and published by . This book was released on 1994 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spanning Trees and Optimization Problems written by Bang Ye Wu and published by CRC Press. This book was released on 2004-01-27 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under
Download or read book Parallel Merge Sort written by Richard Cole and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel computing is an increasingly important area for computer science, and 'Parallel Merge Sort' offers a detailed analysis of this powerful algorithm. With clear explanations and insightful examples, Richard Cole introduces readers to the basics of parallel computing and demonstrates how merge sort can be used to solve complex problems. Whether you are a student or a seasoned professional, this book is an indispensable resource for understanding the power and potential of parallel computing. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book A distributed algorithm for constructing minimal spanning trees in computer communication networks written by Stanford University Stanford Electronics Laboratories. Digital Systems Laboratory and published by . This book was released on 1976 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a distributed algorithm for constructing minimal spanning trees in computer-communication networks. The algorithm can be executed concurrently and asynchronously by the different computers of the network. This algorithm is also suitable for constructing minimal spanning trees using a multiprocessor computer system. There are many reasons for constructing minimal spanning trees in computer-communication networks since minimal spanning tree routing is useful in distributed operating systems for performing broadcast, in adaptive routing algorithms for transmitting delay estimates, and in other networks like the Packet Radio Network.
Download or read book Parallel Algorithms written by M H Alsuwaiyel and published by World Scientific. This book was released on 2022-05-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of parallel algorithms and the underpinning techniques to realize the parallelization. The emphasis is on designing algorithms within the timeless and abstracted context of a high-level programming language. The focus of the presentation is on practical applications of the algorithm design using different models of parallel computation. Each model is illustrated by providing an adequate number of algorithms to solve some problems that quite often arise in many applications in science and engineering.The book is largely self-contained, presuming no special knowledge of parallel computers or particular mathematics. In addition, the solutions to all exercises are included at the end of each chapter.The book is intended as a text in the field of the design and analysis of parallel algorithms. It includes adequate material for a course in parallel algorithms at both undergraduate and graduate levels.
