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Book Design and Implementation of Parallel Graph Algorithms for Minimum Spanning Tree  List Ranking  and Root Finding on Trees

Download or read book Design and Implementation of Parallel Graph Algorithms for Minimum Spanning Tree List Ranking and Root Finding on Trees written by Sun B. Chung and published by . This book was released on 1998 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Spanning Trees and Optimization Problems

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 187 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 one cover spanning tree properties, classical results, and recent research developments. Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees. With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book will be a welcome addition to your reference shelf whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems

Book BSP Implementation of Boruvka s Minimum Spanning Tree Algorithm

Download or read book BSP Implementation of Boruvka s Minimum Spanning Tree Algorithm written by Ding Chu and published by . This book was released on 2015 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, a parallel Minimum Spanning Tree algorithm (MST) is implemented under a Bulk Synchronous Parallel (BSP) graph computation platform. Given a graph with positive weights, MST problem is to find a minimum weight set of edges that connects all of the vertices. MST has been an interesting topic of graph theory for a long time and it has many applications: network design, approximation algorithm of Steiner Tree, cluster analysis, etc. There are classic algorithms of finding the MST. When it comes to the big graph, however, these options do not work very well. In the last decade, many efficient frameworks of dealing big data have been proposed: MapReduce, Pregel, etc. Moreover, the BSP graph processing system makes it possible to run the parallel graph algorithms even in a single machine. In this study, a parallel MST algorithm is implemented based on a BSP-like graph processing platform. In the implementation, there are some classic parallel algorithm design issues: leader selection, information synchronization, etc. One concrete example is provided to go through all the algorithm details. A detailed experimental evaluation is also attached which shows the algorithm performance and possible direction for future improvement.

Book Boruvka Minimum Spanning Tree Parallel Algorithm  with Applications to Satellite Networks

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.

Book Dissertation Abstracts International

Download or read book Dissertation Abstracts International written by and published by . This book was released on 1999 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book A Linear work Parallel Algorithm for Finding Minimum Spanning Trees

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."

Book Simple Parallel Algorithms for the Replacement Edge Problem and Related Problems on Minimum Spanning Trees

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."

Book Parallel Implementation of a Minimum Spanning Tree Algorithm

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.

Book Parallel Implementation of Bor  vka s Minimum Spanning Tree Algorithm

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."

Book American Doctoral Dissertations

Download or read book American Doctoral Dissertations written by and published by . This book was released on 1998 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Parallel Update of Minimum Spanning Trees in Logarithmic Time

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.

Book Sequential and Parallel Algorithms and Data Structures

Download or read book Sequential and Parallel Algorithms and Data Structures written by Peter Sanders and published by Springer Nature. This book was released on 2019-08-31 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a concise introduction to the basic toolbox of structures that allow efficient organization and retrieval of data, key algorithms for problems on graphs, and generic techniques for modeling, understanding, and solving algorithmic problems. The authors aim for a balance between simplicity and efficiency, between theory and practice, and between classical results and the forefront of research. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, optimization, collective communication and computation, and load balancing. The authors also discuss important issues such as algorithm engineering, memory hierarchies, algorithm libraries, and certifying algorithms. Moving beyond the sequential algorithms and data structures of the earlier related title, this book takes into account the paradigm shift towards the parallel processing required to solve modern performance-critical applications and how this impacts on the teaching of algorithms. The book is suitable for undergraduate and graduate students and professionals familiar with programming and basic mathematical language. Most chapters have the same basic structure: the authors discuss a problem as it occurs in a real-life situation, they illustrate the most important applications, and then they introduce simple solutions as informally as possible and as formally as necessary so the reader really understands the issues at hand. As they move to more advanced and optional issues, their approach gradually leads to a more mathematical treatment, including theorems and proofs. The book includes many examples, pictures, informal explanations, and exercises, and the implementation notes introduce clean, efficient implementations in languages such as C++ and Java.

Book Spanning Tree Results For Graphs And Multigraphs  A Matrix theoretic Approach

Download or read book Spanning Tree Results For Graphs And Multigraphs A Matrix theoretic Approach written by John T Saccoman and published by World Scientific. This book was released on 2014-09-04 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theoretic approach to the calculation of the number of spanning trees.The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all stripes, including mathematicians, computer scientists, electrical and computer engineers, and operations researchers.

Book On the Design of an Implementation of Kinetic Minimum Spanning Trees

Download or read book On the Design of an Implementation of Kinetic Minimum Spanning Trees written by Erik-Augund Kvam Garí and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this project, we design a possible implementation of kinetic minimum spanning trees proposed theoretically by Agarwal et al. in 'Parametric and kinetic minimum spanning trees'. The problem we try to solve with this proposal is to maintain a minimum spanning tree of an edge-weighted graph that changes through time. The possible changes in the graph come from changes in the edge weights -which are functions of a parameter t which represents time- in addition to permitting additions and deletions of vertices and edges and updates to the edge weight calculation function.

Book Finding Socially Best Spanning Trees

Download or read book Finding Socially Best Spanning Trees written by Andreas Darmann and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper combines social choice theory with discrete optimization. We assume that individuals have preferences over edges of a graph that need to be aggregated. The goal is to find a socially "best" spanning tree in the graph. As ranking all spanning trees is becoming infeasible even for small numbers of vertices and/or edges of a graph, our interest lies in finding algorithms that determine a socially "best" spanning tree in a simple manner. This problem is closely related to the minimum (or maximum) spanning tree problem in combinatorial optimization. Our main result shows that for the various underlying ranking rules on the set of spanning trees discussed in this paper the sets of "best" spanning trees coincide. Moreover, a greedy algorithm based on a transitive group ranking on the set of edges will always provide such a best spanning tree.

Book Parallel Algorithms for Regular Architectures

Download or read book Parallel Algorithms for Regular Architectures written by Russ Miller and published by MIT Press. This book was released on 1996 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel-Algorithms for Regular Architectures is the first book to concentrate exclusively on algorithms and paradigms for programming parallel computers such as the hypercube, mesh, pyramid, and mesh-of-trees.