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.
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