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An Approximate Algorithm for Solving the Watchman Route Problem

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Robot Vision (RobVis 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4931))

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Abstract

The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is an \({\cal O}(n^3 \log n)\) runtime algorithm (with inherent numerical problems of its implementation). This paper gives an \(\kappa(\varepsilon)\times {\cal O}(kn)\) approximate algorithm for WRP by using a rubberband algorithm, where n is the number of vertices of the simple polygon, k the number of essential cuts, ε the chosen accuracy constant for the minimization of the calculated route, and κ(ε) equals the length of the initial route minus the length of the calculated route, divided by ε.

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Authors and Affiliations

  1. Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700, AV Groningen, The Netherlands

    Fajie Li & Reinhard Klette

  2. Computer Science Department, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Fajie Li & Reinhard Klette

Authors
  1. Fajie Li
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  2. Reinhard Klette
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Gerald Sommer Reinhard Klette

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Li, F., Klette, R. (2008). An Approximate Algorithm for Solving the Watchman Route Problem. In: Sommer, G., Klette, R. (eds) Robot Vision. RobVis 2008. Lecture Notes in Computer Science, vol 4931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78157-8_15

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  • DOI: https://doi.org/10.1007/978-3-540-78157-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78156-1

  • Online ISBN: 978-3-540-78157-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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