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Graphs, Dioids and Semirings

2008-05-14 Business & Economics
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Release : 2008-05-14
Genre : Business & Economics
Kind : eBook
Book Rating : 504/5 ( reviews)

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Book Synopsis Graphs, Dioids and Semirings by : Michel Gondran

Download or read book Graphs, Dioids and Semirings written by Michel Gondran. This book was released on 2008-05-14. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this essential text is to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties. It does so at the same time as demonstrating the modeling and problem-solving flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures which either extend usual algebra or form a new branch of it.

Algebraic Methodology and Software Technology

2011-01-14 Computers
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Release : 2011-01-14
Genre : Computers
Kind : eBook
Book Rating : 956/5 ( reviews)

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Book Synopsis Algebraic Methodology and Software Technology by : Michael Johnson

Download or read book Algebraic Methodology and Software Technology written by Michael Johnson. This book was released on 2011-01-14. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Algebraic Methodology and Software Technology, AMAST 2010, held in Lac-Beauport, QC, Canada, in June 2010. The 14 revised full papers presented were carefully reviewed and selected from 33 submissions. The papers are organized in 1 invited paper, 10 contributed research papers, and 4 system demonstrations.

Semirings as Building Blocks in Cryptography

2019-11-12 Mathematics
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Release : 2019-11-12
Genre : Mathematics
Kind : eBook
Book Rating : 315/5 ( reviews)

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Book Synopsis Semirings as Building Blocks in Cryptography by : Mariana Durcheva

Download or read book Semirings as Building Blocks in Cryptography written by Mariana Durcheva. This book was released on 2019-11-12. Available in PDF, EPUB and Kindle. Book excerpt: Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.

Path Problems in Networks

2022-06-01 Computers
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Release : 2022-06-01
Genre : Computers
Kind : eBook
Book Rating : 836/5 ( reviews)

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Book Synopsis Path Problems in Networks by : John Baras

Download or read book Path Problems in Networks written by John Baras. This book was released on 2022-06-01. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path problem, and an exposition of a broad range of applications. First of all, the shortest path problem is presented so as to fix terminology and concepts: existence and uniqueness of solutions, robustness to parameter changes, and centralized and distributed computation algorithms. Then, these concepts are generalized to the algebraic context of semirings. Methods for creating new semirings, useful for modeling new problems, are provided. A large part of the book is then devoted to numerous applications of the algebraic path problem, ranging from mobile network routing to BGP routing to social networks. These applications show what kind of problems can be modeled as algebraic path problems; they also serve as examples on how to go about modeling new problems. This monograph will be useful to network researchers, engineers, and graduate students. It can be used either as an introduction to the topic, or as a quick reference to the theoretical facts, algorithms, and application examples. The theoretical background assumed for the reader is that of a graduate or advanced undergraduate student in computer science or engineering. Some familiarity with algebra and algorithms is helpful, but not necessary. Algebra, in particular, is used as a convenient and concise language to describe problems that are essentially combinatorial. Table of Contents: Classical Shortest Path / The Algebraic Path Problem / Properties and Computation of Solutions / Applications / Related Areas / List of Semirings and Applications

Tropical and Idempotent Mathematics

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 821/5 ( reviews)

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Book Synopsis Tropical and Idempotent Mathematics by : Grigoriĭ Lazarevich Litvinov

Download or read book Tropical and Idempotent Mathematics written by Grigoriĭ Lazarevich Litvinov. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade. Tropical mathematics can be viewed as a result of the Maslov dequantization applied to 'traditional' mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks. Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.

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