Euclidean Shortest Paths

This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.

This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.

Reviews algorithms for the exact or approximate solution of Euclidean shortest-path problems, with a specific focus on rubberband algorithms Provides theoretical and programming exercises at the end of each chapter Discusses each concept and algorithm in depth, including mathematical proofs for many of the given statements Includes supplementary material: sn.pub/extras

Texte du rabat

The Euclidean shortest path (ESP) problem asks the question: what is the path of minimum length connecting two points in a 2- or 3-dimensional space? Variants of this industrially-significant computational geometry problem also require the path to pass through specified areas and avoid defined obstacles.

This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Suitable for a second- or third-year university algorithms course, the text enables readers to understand not only the algorithms and their pseudocodes, but also the correctness proofs, the analysis of time complexities, and other related topics.

Topics and features:

• Provides theoretical and programming exercises at the end of each chapter
• Presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms
• Discusses algorithms for calculating exact or approximate ESPs in the plane
• Examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves
• Describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems
• Includes lists of symbols and abbreviations, in addition to other appendices This hands-on guide will be of interest to undergraduate students in computer science, IT, mathematics, and engineering. Programmers, mathematicians, and engineers dealing with shortest-path problems in practical applications will also find the book a useful resource.

Dr. Fajie Li is at Huaqiao University, Xiamen, Fujian, China. Prof. Dr. Reinhard Klette is at the Tamaki Innovation Campus of The University of Auckland.

Contenu

Part I: Discrete or Continuous Shortest Paths.- Euclidean Shortest Paths.- Deltas and Epsilons.- Rubberband Algorithms.- Part II: Paths in the Plane.- Convex Hulls in the Plane.- Partitioning a Polygon or the Plane.- Approximate ESP Algorithms.- Part III: Paths in Three-Dimensional Space.- Paths on Surfaces.- Paths in Simple Polyhedrons.- Paths in Cube Curves.- Part IV: Art Galleries.- Touring Polygons.- Watchman Route.- Safari and Zookeeper Problems.