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Author: Ravindra K. Ahuja Publisher: ISBN: 9781332260768 Category : Mathematics Languages : en Pages : 48
Book Description
Excerpt from Faster Algorithms for the Shortest Path Problem In this paper, we present the fastest known algorithms for the shortest path problem with nonnegative integer arc lengths We consider networks with n nodes and m arcs and in which C represents the largest arc length in the network. Our algorithms are obtained by implementing Dijkstra's algorithm using a new data structure which we call a redistributive heap The one-level redistributive heap consists of O(log C) buckets, each with an associated range of integer numbers Each bucket stores nodes whose temporary distance labels lie in its range Further, the ranges are dynamically changed during the execution, which leads to a redistribution of nodes to buckets. The resulting algorithm runs in O(m + n log C) time. Using a two-level redistributive heap, we improve the complexity of this algorithm to O(m + n log C/ log log nC). Finally, we use a modified version of Fibonacci heaps to reduce the complexity of our algorithm to O(m + n log C ). This algorithm, under the assumption that the largest arc length is bounded by a polynomial function of n, runs in O(m + n log n ) time, which improves over the best previous strongly polynomial bound of O(m + n log n) due to Fredman and Tarjan. We also analyse our algorithms in the semi-logarithmic model of computation. In this model, it takes [log x/log n] time to perform arithmetic on integers of value x. It is shown that in this model of computation, some of our algorithms run in linear time for sufficiently large values of C. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Author: Ravindra K. Ahuja Publisher: ISBN: 9781332260768 Category : Mathematics Languages : en Pages : 48
Book Description
Excerpt from Faster Algorithms for the Shortest Path Problem In this paper, we present the fastest known algorithms for the shortest path problem with nonnegative integer arc lengths We consider networks with n nodes and m arcs and in which C represents the largest arc length in the network. Our algorithms are obtained by implementing Dijkstra's algorithm using a new data structure which we call a redistributive heap The one-level redistributive heap consists of O(log C) buckets, each with an associated range of integer numbers Each bucket stores nodes whose temporary distance labels lie in its range Further, the ranges are dynamically changed during the execution, which leads to a redistribution of nodes to buckets. The resulting algorithm runs in O(m + n log C) time. Using a two-level redistributive heap, we improve the complexity of this algorithm to O(m + n log C/ log log nC). Finally, we use a modified version of Fibonacci heaps to reduce the complexity of our algorithm to O(m + n log C ). This algorithm, under the assumption that the largest arc length is bounded by a polynomial function of n, runs in O(m + n log n ) time, which improves over the best previous strongly polynomial bound of O(m + n log n) due to Fredman and Tarjan. We also analyse our algorithms in the semi-logarithmic model of computation. In this model, it takes [log x/log n] time to perform arithmetic on integers of value x. It is shown that in this model of computation, some of our algorithms run in linear time for sufficiently large values of C. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Author: Sloan School Of Management Publisher: Hardpress Publishing ISBN: 9781314922202 Category : Languages : en Pages : 54
Book Description
Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Author: Ravindra K Ahuja Publisher: Andesite Press ISBN: 9781298827487 Category : Languages : en Pages : 48
Book Description
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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
Author: Neal E. Young Publisher: Forgotten Books ISBN: 9780656033829 Category : Mathematics Languages : en Pages : 38
Book Description
Excerpt from Faster Parametric Shortest Path and Minimum Balance Algorithms The second section describes the minimum mean cycle problem and how the parametric shortest path algorithm can be used to solve it. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Sloan School Of Management Publisher: Nabu Press ISBN: 9781294451549 Category : Languages : en Pages : 48
Book Description
This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Author: Wolfgang Thomas Publisher: Springer ISBN: 3540709185 Category : Computers Languages : en Pages : 723
Book Description
This book constitutes the refereed proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007, held in Aachen, Germany in February 2007. The 56 revised full papers presented together with 3 invited papers address the whole range of theoretical computer science as well as current challenges like biological computing, quantum computing, and mobile and net computing.
Author: Hector Ortega-Arranz Publisher: Morgan & Claypool Publishers ISBN: 1627055401 Category : Computers Languages : en Pages : 89
Book Description
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.
Author: Neal E Young Publisher: Palala Press ISBN: 9781341787416 Category : Languages : en Pages : 40
Book Description
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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. 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.
Author: Hector Ortega-Arranz Publisher: Springer Nature ISBN: 3031025741 Category : Mathematics Languages : en Pages : 71
Book Description
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
Author: Ravindra K. Ahuja
Author: Ravindra K. Ahuja
Author: Sloan School Of Management
Author: Ravindra K Ahuja
Author: Neal E. Young
Author: Sloan School Of Management
Author: 
Author: Wolfgang Thomas
Author: Hector Ortega-Arranz
Author: Neal E Young
Author: Hector Ortega-Arranz