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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.

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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.

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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

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From the book reviews:

"This book presents selected algorithms for the exact or approximate solution of several variants of the Euclidean shortest path problem (ESP). ... The book has been successful in addressing the Euclidean Shortest Path problems by presenting exact and approximate algorithms in the light of rubberband algorithms, and will be immensely useful to students and researchers in the area." (Arindam Biswas, IAPR Newsletter, Vol. 37 (1), January, 2015)

"Li (Huaqiao Univ., China) and Klette (Univ. of Auckland, New Zealand) have written an interesting and very reader-friendly book on algorithms that find a shortest path between two vertices of a graph. ... this is the first book-length treatment of the topic. The entire text is accessible to advanced undergraduates. ... Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and researchers/faculty." (M. Bona, Choice, Vol. 49 (9), May, 2012)

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