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  • © 2011

Euclidean Shortest Paths

Exact or Approximate Algorithms

  • 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

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XVII
  2. Discrete or Continuous Shortest Paths

    1. Front Matter

      Pages 1-1
    2. Euclidean Shortest Paths

      • Fajie Li, Reinhard Klette
      Pages 3-29
    3. Deltas and Epsilons

      • Fajie Li, Reinhard Klette
      Pages 31-51
    4. Rubberband Algorithms

      • Fajie Li, Reinhard Klette
      Pages 53-89
  3. Paths in the Plane

    1. Front Matter

      Pages 91-91
    2. Convex Hulls in the Plane

      • Fajie Li, Reinhard Klette
      Pages 93-125
    3. Partitioning a Polygon or the Plane

      • Fajie Li, Reinhard Klette
      Pages 127-169
    4. ESPs in Simple Polygons

      • Fajie Li, Reinhard Klette
      Pages 171-187
  4. Paths in 3-Dimensional Space

    1. Front Matter

      Pages 189-189
    2. Paths on Surfaces

      • Fajie Li, Reinhard Klette
      Pages 191-211
    3. Paths in Simple Polyhedrons

      • Fajie Li, Reinhard Klette
      Pages 213-230
    4. Paths in Cube-Curves

      • Fajie Li, Reinhard Klette
      Pages 231-309
  5. Art Galleries

    1. Front Matter

      Pages 311-311
    2. Touring Polygons

      • Fajie Li, Reinhard Klette
      Pages 313-325
    3. Watchman Routes

      • Fajie Li, Reinhard Klette
      Pages 327-345
    4. Safari and Zookeeper Problems

      • Fajie Li, Reinhard Klette
      Pages 347-361
  6. Back Matter

    Pages 363-376

About this book

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

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)

Authors and Affiliations

  • School of Information Science & Technol., Huaqiao University, Xiamen, China, People's Republic

    Fajie Li

  • Dept. Computer Science, University of Auckland, Auckland, New Zealand

    Reinhard Klette

Bibliographic Information

Buy it now

Buying options

eBook USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access