Euclidean Shortest Paths

Exact or Approximate Algorithms

  • Fajie Li
  • Reinhard Klette

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Discrete or Continuous Shortest Paths

    1. Front Matter
      Pages 1-1
    2. Fajie Li, Reinhard Klette
      Pages 3-29
    3. Fajie Li, Reinhard Klette
      Pages 31-51
    4. Fajie Li, Reinhard Klette
      Pages 53-89
  3. Paths in the Plane

    1. Front Matter
      Pages 91-91
    2. Fajie Li, Reinhard Klette
      Pages 93-125
    3. Fajie Li, Reinhard Klette
      Pages 127-169
    4. Fajie Li, Reinhard Klette
      Pages 171-187
  4. Paths in 3-Dimensional Space

    1. Front Matter
      Pages 189-189
    2. Fajie Li, Reinhard Klette
      Pages 191-211
    3. Fajie Li, Reinhard Klette
      Pages 213-230
    4. Fajie Li, Reinhard Klette
      Pages 231-309
  5. Art Galleries

    1. Front Matter
      Pages 311-311
    2. Fajie Li, Reinhard Klette
      Pages 313-325
    3. Fajie Li, Reinhard Klette
      Pages 327-345
    4. Fajie Li, Reinhard Klette
      Pages 347-361
  6. Back Matter
    Pages 363-376

About this book


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.


Art Gallery Problems Computational Geometry Cube Curves Euclidean Shortest Path Parts Cutting Problem Rubberband Algorithm Safari Problem Simple Polygon Surface of Polytope Touring Polygons Watchman Route Problem Zookeeper Problem q-Rectangles

Authors and affiliations

  • Fajie Li
    • 1
  • Reinhard Klette
    • 2
  1. 1.School of Information Science & Technol.Huaqiao UniversityXiamenChina, People's Republic
  2. 2.Dept. Computer ScienceUniversity of AucklandAucklandNew Zealand

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-4471-2255-5
  • Online ISBN 978-1-4471-2256-2
  • Buy this book on publisher's site