Path problems in networks
By: John S. Baras, George Theodorakopoulos
Contributors: Theodorakopoulos, George
Series: Synthesis lectures on communication networks -- # 3
Publisher: Morgan & Claypool Publishers
Published: 2010
Place of publication: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA)
Language: eng
Format: [electronic resource] /
ISBN-13: 9781598299243; 9781598299236
Subjects: Computer networks; Semirings (Mathematics); Routing protocols (Computer network protocols); Mathematical models
Other titles: Synthesis digital library of engineering and computer science.
Description: 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.
Notes: Part of: Synthesis digital library of engineering and computer science.

Title from PDF t.p. (viewed on February 16, 2010).

Series from website.

Includes bibliographical references (p. 61-64).

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat reader.
Table of contents: title: 1. Classical shortest path; title: Definitions and problem description; title: Computation of shortest paths; title: Distributed computation of shortest paths; title: 2. The algebraic path problem; title: Semirings and the algebraic path problem; title: Creating new semirings; title: 3. Properties and computation of solutions; title: Alternative viewpoints: paths and matrices; title: Edge sensitivities; title: Centralized computation of A*; title: Decentralized computation of A*; title: 4. Applications; title: Path enumeration; title: Expectation semirings; title: Minimum weight spanning tree; title: Longest path; title: Quality of service (QoS) routing; title: BGP routing; title: Shortest path with time-inhomogeneous edges; title: Network reliability; title: Shortest paths with gains/losses on the edges; title: Trust-reputation; title: Social networks; title: Traffic assignment; title: Applications of sensitivity analysis; title: 5. Related areas; title: Non-semiring path problems; title: Semiring non-path problems; title: 6. List of semirings and applications; title: Authors' biographies.