The Shortest-Path Problem: Analysis and Comparison of Methods [Paperback]

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' BiographiesList 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 .Hector Ortega-Arranz received his M.S. in Computer Science Engineering, and his M.S. in Research in Information and Communication Technologies, from the Universidad de Valladolid, Spain, in 2010 and 2011, respectively. He is currently a researcher and a Ph.D. candidate in the Department of Computer Science of this university. His research interests include shortest-path algorithms, parallel and distributed computing, and GPU compul“2