R - Heaps with Suspended Relaxation for Manipulating Priority Queues and a New Algorithm for Reweighting Graphs

R - Heaps with Suspended Relaxation for Manipulating Priority Queues and a New Algorithm for Reweighting Graphs

Author: Ruth Shrairman

Publisher: Universal-Publishers

Published: 2004-12

Total Pages: 144

ISBN-13: 1581122365

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This research is dedicated to two main problems in finding shortest paths in the graphs. The first problem is to find shortest paths from an origin to all other vertices in non-negatively weighted graph. The second problem is the same, except it is allowed that some edges are negative. This is a more difficult problem that can be solved by relatively complicated algorithms. We attack the first problem by introducing a new data structure - Relaxed Heaps that implements efficiently two main operations critical for the improvement of Dijkstra's shortest path algorithm. R2-heaps with suspended relaxation proposed in this research gives the best known worst-case time bounds of O(1) for a decrease_key operation and O(logn) for a delete_min operation. That results in the best worst-case running time for Dijkstra's algorithm O(m+nlogn), and represents an improvement over Fibonacci Heaps, which give the same, but amortized time bounds. The new data structure is simple and efficient in practical implementation. The empirical study with R2-heaps demonstrated strong advantage of its use for Dijkstra's algorithm over the "raw" Dijkstra's without heaps. This advantage is especially dramatic for sparse graphs. R2-heaps can be used in a large number of applications in which set manipulations should be implemented efficiently. For the problem of finding shortest paths in graphs with some negative edges, we present a new approach of reweighting graphs by first reducing the graph to its canonical form, which allows to apply an effective algorithm to reweight the graph to one with non-negative edges only and simultaneously to find shortest paths from an origin to all other vertices in the graph. This approach allows to give new algebraic and geometric interpretations of the problem. The experiment with the Sweeping Algorithm demonstrated O(n? logn) expected time complexity. These results open new prospects to improve algorithms for a wide variety of problems including different network optimization problems that use Dijkstra's algorithm as a subroutine, as well as multiple Operations Research and Modeling problems that can be reduced to finding shortest paths on graphs.


Book Synopsis R - Heaps with Suspended Relaxation for Manipulating Priority Queues and a New Algorithm for Reweighting Graphs by : Ruth Shrairman

Download or read book R - Heaps with Suspended Relaxation for Manipulating Priority Queues and a New Algorithm for Reweighting Graphs written by Ruth Shrairman and published by Universal-Publishers. This book was released on 2004-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research is dedicated to two main problems in finding shortest paths in the graphs. The first problem is to find shortest paths from an origin to all other vertices in non-negatively weighted graph. The second problem is the same, except it is allowed that some edges are negative. This is a more difficult problem that can be solved by relatively complicated algorithms. We attack the first problem by introducing a new data structure - Relaxed Heaps that implements efficiently two main operations critical for the improvement of Dijkstra's shortest path algorithm. R2-heaps with suspended relaxation proposed in this research gives the best known worst-case time bounds of O(1) for a decrease_key operation and O(logn) for a delete_min operation. That results in the best worst-case running time for Dijkstra's algorithm O(m+nlogn), and represents an improvement over Fibonacci Heaps, which give the same, but amortized time bounds. The new data structure is simple and efficient in practical implementation. The empirical study with R2-heaps demonstrated strong advantage of its use for Dijkstra's algorithm over the "raw" Dijkstra's without heaps. This advantage is especially dramatic for sparse graphs. R2-heaps can be used in a large number of applications in which set manipulations should be implemented efficiently. For the problem of finding shortest paths in graphs with some negative edges, we present a new approach of reweighting graphs by first reducing the graph to its canonical form, which allows to apply an effective algorithm to reweight the graph to one with non-negative edges only and simultaneously to find shortest paths from an origin to all other vertices in the graph. This approach allows to give new algebraic and geometric interpretations of the problem. The experiment with the Sweeping Algorithm demonstrated O(n? logn) expected time complexity. These results open new prospects to improve algorithms for a wide variety of problems including different network optimization problems that use Dijkstra's algorithm as a subroutine, as well as multiple Operations Research and Modeling problems that can be reduced to finding shortest paths on graphs.

American Doctoral Dissertations

American Doctoral Dissertations

Author:

Publisher:

Published: 1995

Total Pages: 896

ISBN-13:

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Book Synopsis American Doctoral Dissertations by :

Download or read book American Doctoral Dissertations written by and published by . This book was released on 1995 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Shortest-Path Problem

The Shortest-Path Problem

Author: Hector Ortega-Arranz

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 71

ISBN-13: 3031025741

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Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology. Table of Contents: List of Figures / List of Tables / Acknowledgments / Introduction / Graph Theory Basics / Classical Algorithms / Hierarchical Preprocessing-Dependent Approaches / Non-Hierarchical Preprocessing-Dependent Approaches / Analysis and Comparison of Approaches / Conclusions / Bibliography / Authors' Biographies


Book Synopsis The Shortest-Path Problem by : Hector Ortega-Arranz

Download or read book The Shortest-Path Problem written by Hector Ortega-Arranz and published by Springer Nature. This book was released on 2022-05-31 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology. Table of Contents: List of Figures / List of Tables / Acknowledgments / Introduction / Graph Theory Basics / Classical Algorithms / Hierarchical Preprocessing-Dependent Approaches / Non-Hierarchical Preprocessing-Dependent Approaches / Analysis and Comparison of Approaches / Conclusions / Bibliography / Authors' Biographies

Introduction to Information Retrieval

Introduction to Information Retrieval

Author: Christopher D. Manning

Publisher: Cambridge University Press

Published: 2008-07-07

Total Pages:

ISBN-13: 1139472100

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Class-tested and coherent, this textbook teaches classical and web information retrieval, including web search and the related areas of text classification and text clustering from basic concepts. It gives an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections. All the important ideas are explained using examples and figures, making it perfect for introductory courses in information retrieval for advanced undergraduates and graduate students in computer science. Based on feedback from extensive classroom experience, the book has been carefully structured in order to make teaching more natural and effective. Slides and additional exercises (with solutions for lecturers) are also available through the book's supporting website to help course instructors prepare their lectures.


Book Synopsis Introduction to Information Retrieval by : Christopher D. Manning

Download or read book Introduction to Information Retrieval written by Christopher D. Manning and published by Cambridge University Press. This book was released on 2008-07-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Class-tested and coherent, this textbook teaches classical and web information retrieval, including web search and the related areas of text classification and text clustering from basic concepts. It gives an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections. All the important ideas are explained using examples and figures, making it perfect for introductory courses in information retrieval for advanced undergraduates and graduate students in computer science. Based on feedback from extensive classroom experience, the book has been carefully structured in order to make teaching more natural and effective. Slides and additional exercises (with solutions for lecturers) are also available through the book's supporting website to help course instructors prepare their lectures.

Ray Tracing Gems

Ray Tracing Gems

Author: Eric Haines

Publisher: Apress

Published: 2019-02-25

Total Pages: 622

ISBN-13: 1484244273

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This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for:Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPUs


Book Synopsis Ray Tracing Gems by : Eric Haines

Download or read book Ray Tracing Gems written by Eric Haines and published by Apress. This book was released on 2019-02-25 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for:Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPUs

Heuristic Search

Heuristic Search

Author: Stefan Edelkamp

Publisher: Elsevier

Published: 2011-05-31

Total Pages: 712

ISBN-13: 9780080919737

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Search has been vital to artificial intelligence from the very beginning as a core technique in problem solving. The authors present a thorough overview of heuristic search with a balance of discussion between theoretical analysis and efficient implementation and application to real-world problems. Current developments in search such as pattern databases and search with efficient use of external memory and parallel processing units on main boards and graphics cards are detailed. Heuristic search as a problem solving tool is demonstrated in applications for puzzle solving, game playing, constraint satisfaction and machine learning. While no previous familiarity with heuristic search is necessary the reader should have a basic knowledge of algorithms, data structures, and calculus. Real-world case studies and chapter ending exercises help to create a full and realized picture of how search fits into the world of artificial intelligence and the one around us. Provides real-world success stories and case studies for heuristic search algorithms Includes many AI developments not yet covered in textbooks such as pattern databases, symbolic search, and parallel processing units


Book Synopsis Heuristic Search by : Stefan Edelkamp

Download or read book Heuristic Search written by Stefan Edelkamp and published by Elsevier. This book was released on 2011-05-31 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Search has been vital to artificial intelligence from the very beginning as a core technique in problem solving. The authors present a thorough overview of heuristic search with a balance of discussion between theoretical analysis and efficient implementation and application to real-world problems. Current developments in search such as pattern databases and search with efficient use of external memory and parallel processing units on main boards and graphics cards are detailed. Heuristic search as a problem solving tool is demonstrated in applications for puzzle solving, game playing, constraint satisfaction and machine learning. While no previous familiarity with heuristic search is necessary the reader should have a basic knowledge of algorithms, data structures, and calculus. Real-world case studies and chapter ending exercises help to create a full and realized picture of how search fits into the world of artificial intelligence and the one around us. Provides real-world success stories and case studies for heuristic search algorithms Includes many AI developments not yet covered in textbooks such as pattern databases, symbolic search, and parallel processing units

Meta-Learning in Decision Tree Induction

Meta-Learning in Decision Tree Induction

Author: Krzysztof Grąbczewski

Publisher: Springer

Published: 2013-09-11

Total Pages: 349

ISBN-13: 3319009605

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The book focuses on different variants of decision tree induction but also describes the meta-learning approach in general which is applicable to other types of machine learning algorithms. The book discusses different variants of decision tree induction and represents a useful source of information to readers wishing to review some of the techniques used in decision tree learning, as well as different ensemble methods that involve decision trees. It is shown that the knowledge of different components used within decision tree learning needs to be systematized to enable the system to generate and evaluate different variants of machine learning algorithms with the aim of identifying the top-most performers or potentially the best one. A unified view of decision tree learning enables to emulate different decision tree algorithms simply by setting certain parameters. As meta-learning requires running many different processes with the aim of obtaining performance results, a detailed description of the experimental methodology and evaluation framework is provided. Meta-learning is discussed in great detail in the second half of the book. The exposition starts by presenting a comprehensive review of many meta-learning approaches explored in the past described in literature, including for instance approaches that provide a ranking of algorithms. The approach described can be related to other work that exploits planning whose aim is to construct data mining workflows. The book stimulates interchange of ideas between different, albeit related, approaches.


Book Synopsis Meta-Learning in Decision Tree Induction by : Krzysztof Grąbczewski

Download or read book Meta-Learning in Decision Tree Induction written by Krzysztof Grąbczewski and published by Springer. This book was released on 2013-09-11 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on different variants of decision tree induction but also describes the meta-learning approach in general which is applicable to other types of machine learning algorithms. The book discusses different variants of decision tree induction and represents a useful source of information to readers wishing to review some of the techniques used in decision tree learning, as well as different ensemble methods that involve decision trees. It is shown that the knowledge of different components used within decision tree learning needs to be systematized to enable the system to generate and evaluate different variants of machine learning algorithms with the aim of identifying the top-most performers or potentially the best one. A unified view of decision tree learning enables to emulate different decision tree algorithms simply by setting certain parameters. As meta-learning requires running many different processes with the aim of obtaining performance results, a detailed description of the experimental methodology and evaluation framework is provided. Meta-learning is discussed in great detail in the second half of the book. The exposition starts by presenting a comprehensive review of many meta-learning approaches explored in the past described in literature, including for instance approaches that provide a ranking of algorithms. The approach described can be related to other work that exploits planning whose aim is to construct data mining workflows. The book stimulates interchange of ideas between different, albeit related, approaches.

Algorithms in Bioinformatics

Algorithms in Bioinformatics

Author: Olivier Gascuel

Publisher: Springer

Published: 2003-05-15

Total Pages: 317

ISBN-13: 3540446966

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This book constitutes the refereed proceedings of the First International Workshop on Algorithms in Bioinformatics, WABI 2001, held in Aarhus, Denmark, in August 2001. The 23 revised full papers presented were carefully reviewed and selected from more than 50 submissions. Among the issues addressed are exact and approximate algorithms for genomics, sequence analysis, gene and signal recognition, alignment, molecular evolution, structure determination or prediction, gene expression and gene networks, proteomics, functional genomics, and drug design; methodological topics from algorithmics; high-performance approaches to hard computational problems in bioinformatics.


Book Synopsis Algorithms in Bioinformatics by : Olivier Gascuel

Download or read book Algorithms in Bioinformatics written by Olivier Gascuel and published by Springer. This book was released on 2003-05-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Workshop on Algorithms in Bioinformatics, WABI 2001, held in Aarhus, Denmark, in August 2001. The 23 revised full papers presented were carefully reviewed and selected from more than 50 submissions. Among the issues addressed are exact and approximate algorithms for genomics, sequence analysis, gene and signal recognition, alignment, molecular evolution, structure determination or prediction, gene expression and gene networks, proteomics, functional genomics, and drug design; methodological topics from algorithmics; high-performance approaches to hard computational problems in bioinformatics.

Big Data Optimization: Recent Developments and Challenges

Big Data Optimization: Recent Developments and Challenges

Author: Ali Emrouznejad

Publisher: Springer

Published: 2016-05-26

Total Pages: 487

ISBN-13: 3319302655

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The main objective of this book is to provide the necessary background to work with big data by introducing some novel optimization algorithms and codes capable of working in the big data setting as well as introducing some applications in big data optimization for both academics and practitioners interested, and to benefit society, industry, academia, and government. Presenting applications in a variety of industries, this book will be useful for the researchers aiming to analyses large scale data. Several optimization algorithms for big data including convergent parallel algorithms, limited memory bundle algorithm, diagonal bundle method, convergent parallel algorithms, network analytics, and many more have been explored in this book.


Book Synopsis Big Data Optimization: Recent Developments and Challenges by : Ali Emrouznejad

Download or read book Big Data Optimization: Recent Developments and Challenges written by Ali Emrouznejad and published by Springer. This book was released on 2016-05-26 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this book is to provide the necessary background to work with big data by introducing some novel optimization algorithms and codes capable of working in the big data setting as well as introducing some applications in big data optimization for both academics and practitioners interested, and to benefit society, industry, academia, and government. Presenting applications in a variety of industries, this book will be useful for the researchers aiming to analyses large scale data. Several optimization algorithms for big data including convergent parallel algorithms, limited memory bundle algorithm, diagonal bundle method, convergent parallel algorithms, network analytics, and many more have been explored in this book.

Computer Vision - ACCV 2010

Computer Vision - ACCV 2010

Author: Ron Kimmel

Publisher: Springer

Published: 2011-02-28

Total Pages: 747

ISBN-13: 3642193099

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The four-volume set LNCS 6492-6495 constitutes the thoroughly refereed post-proceedings of the 10th Asian Conference on Computer Vision, ACCV 2009, held in Queenstown, New Zealand in November 2010. All together the four volumes present 206 revised papers selected from a total of 739 Submissions. All current issues in computer vision are addressed ranging from algorithms that attempt to automatically understand the content of images, optical methods coupled with computational techniques that enhance and improve images, and capturing and analyzing the world's geometry while preparing the higher level image and shape understanding. Novel geometry techniques, statistical learning methods, and modern algebraic procedures are dealt with as well.


Book Synopsis Computer Vision - ACCV 2010 by : Ron Kimmel

Download or read book Computer Vision - ACCV 2010 written by Ron Kimmel and published by Springer. This book was released on 2011-02-28 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 6492-6495 constitutes the thoroughly refereed post-proceedings of the 10th Asian Conference on Computer Vision, ACCV 2009, held in Queenstown, New Zealand in November 2010. All together the four volumes present 206 revised papers selected from a total of 739 Submissions. All current issues in computer vision are addressed ranging from algorithms that attempt to automatically understand the content of images, optical methods coupled with computational techniques that enhance and improve images, and capturing and analyzing the world's geometry while preparing the higher level image and shape understanding. Novel geometry techniques, statistical learning methods, and modern algebraic procedures are dealt with as well.