Author: N.B. Singh
Publisher: N.B. Singh
ISBN:
Category : Mathematics
Languages : en
Pages : 132

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Book Description
"Combinatorial Problems: Minimum Spanning Tree" is a beginner-friendly introduction to the concept of Minimum Spanning Trees (MST), a fundamental tool in computer science and engineering. This book provides clear explanations and practical examples to demystify MST algorithms, which are essential for efficiently connecting nodes in various networks while minimizing costs. Aimed at absolute beginners, it covers the basic principles, step-by-step algorithms, and real-world applications of MST in telecommunications, transportation, and more. Whether you're a student, aspiring engineer, or curious reader, this accessible guide equips you with the foundational knowledge to understand and apply MST effectively in solving connectivity challenges across different fields.

Author: Bang Ye Wu
Publisher: CRC Press
ISBN: 0203497287
Category : Computers
Languages : en
Pages : 200

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Book Description
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

Author: Dimitris Bertsimas
Publisher: Forgotten Books
ISBN: 9780265619247
Category : Mathematics
Languages : en
Pages : 48

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Book Description
Excerpt from The Probabilistic Minimum Spanning Tree Problem: Complexity and Combinatorial Properties In this paper we consider a natural probabilistic variation of this classical problem. In particular, we consider the case where not all the points are deterministically present, but are present with certain probability. Formally, given a weighted graph G (v, E) and a probability of presence p(s) for each subset S of V, we want to construct an a priori spanning tree of minimum expected length in the following sense: on any given instance of the problem delete the vertices and their adjacent edges among the set of absent vertices provided that the tree remains connected. The problem of finding an a priori spanning tree of minimum expected length is the probabilistic minimum spanning tree (pmst) problem. In order to clarify the definition of the pmst problem, consider the example in Figure 1. If the a priori tree is T and nodes are the only ones not present, the tree becomes ti. One can easily observe that if every node is present with probability p. 1 for all i E V then the problem reduces to the classical mst problem. 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: Dimitris Bertsimas
Publisher: Legare Street Press
ISBN: 9781019946701
Category :
Languages : en
Pages : 0

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Book Description
Dimitris Bertsimas, an expert in the field of operations research, provides an in-depth exploration of the probabilistic minimum spanning tree problem. With detailed analysis of various algorithms and combinatorial properties, this publication will appeal to researchers and practitioners alike. 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.

Author: Bernhard Korte
Publisher: Springer Science & Business Media
ISBN: 3540718443
Category : Mathematics
Languages : en
Pages : 628

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Book Description
Now fully updated in a third edition, this is a comprehensive textbook on combinatorial optimization. It puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete but concise proofs, also for many deep results, some of which have not appeared in print before. Recent topics are covered as well, and numerous references are provided. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.

Author: Dingzhu Du
Publisher: World Scientific
ISBN: 9812791442
Category : Computers
Languages : en
Pages : 373

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Book Description
The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice.

Author: Ding-Zhu Du
Publisher: Springer Nature
ISBN: 3031105966
Category : Mathematics
Languages : en
Pages : 407

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Book Description
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.

Author: Danny Z. Chen
Publisher: Springer Science & Business Media
ISBN: 3540369252
Category : Computers
Languages : en
Pages : 542

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Book Description
This book presents the refereed proceedings of the 12th Annual International Computing and Combinatorics Conference, COCOON 2006, held in Taipei, Taiwan, August 2006. The book offers 52 revised full papers presented together with abstracts of 2 invited talks. The papers are organized in topical sections on computational economics, finance, and management, graph algorithms, computational complexity and computability, quantum computing, computational biology and medicine, computational geometry, graph theory, and more.

Author: Bang Ye Wu
Publisher: CRC Press
ISBN: 1135437033
Category : Mathematics
Languages : en
Pages : 187

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Book Description
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

Author: Katta G. Murty
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 648

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Book Description
This book covers the significant advances in network flow methods ranging across modeling, applications, algorithms, their implementations, and computational complexity. It deals with the problems faced on network structures that can be handled by linear programming techniques or their adaptations. It is particularly useful for professionals involved in mathematical programming and linear programming in the areas of operations research, industrial engineering, other branches of engineering and business applications.