Titlebook: Euclidean Shortest Paths; Exact or Approximate Fajie Li,Reinhard Klette Book 2011 Springer-Verlag London Limited 2011 Art Gallery Problems.

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Euclidean Shortest PathsThe introductory chapter explains the difference between shortest paths in finite graphs and shortest paths in Euclidean geometry, which is also called ‘the common geometry of our world’. The chapter demonstrates the diversity of such problems, defined between points in a plane, on a surface, or in the 3-dimensional space.

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Deltas and EpsilonsThe introduction ended with recalling concepts in discrete mathematics as used in this book. This second chapter adds further basic concepts in continuous mathematics that are also relevant for this book, especially in the context of approximate algorithms.

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978-1-4471-6064-9Springer-Verlag London Limited 2011

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Fajie Li,Reinhard KletteReviews 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 o

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-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.978-1-4471-6064-9978-1-4471-2256-2

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Andrea Bravo-Doddoli,Rozzana Sánchez-Aragón be) NP-complete or NP-hard 3D ESP problems in time ., where . is the number of layers in a stack, which is introduced in this chapter as being the .. The proposed approximation method has straightforward applications for ESP problems when analysing polyhedral objects (e.g., in 3D imaging), of for ‘

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Paths in Simple Polyhedrons be) NP-complete or NP-hard 3D ESP problems in time ., where . is the number of layers in a stack, which is introduced in this chapter as being the .. The proposed approximation method has straightforward applications for ESP problems when analysing polyhedral objects (e.g., in 3D imaging), of for ‘