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Watchman Routes

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Euclidean Shortest Paths

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Abstract

So far, the best result in running time for solving the floating watchman route problem (i.e., shortest path for viewing any point in a simple polygon with given start point) is \({\mathcal{O}}(n^{4}\log n)\), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. This chapter provides an algorithm with \(\kappa(\varepsilon) \cdot{\mathcal{O}}(kn) + {\mathcal{O}}(k^{2}n)\) runtime, where n is the number of vertices of the given simple polygon P, and k the number of essential cuts; κ(ε) defines the numerical accuracy depending on a selected constant ε>0. Moreover, the presented RBA appears to be significantly simpler, easier to understand and to be implemented than previous ones for solving the fixed watchman route problem.

Sometimes the path you are on is not as important as the direction you are heading. For, no matter if you take the Holland Tunnel or the George Washington Bridge you get to New Jersey, so long as you are heading west. The procedure involved in your path to Nirvana may meander, but a road worth travelling will have its twists and turns.

Kevin Patrick Smith (born 1970)

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Notes

  1. 1.

    We do not have to consider any non-essential cuts when defining active cuts. Otherwise the route would be longer.

  2. 2.

    See [29].

  3. 3.

    See [30].

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Authors and Affiliations

  1. School of Information Science and Technology, Huaqiao University, P.O. Box 800, Xiamen, Fujian, People’s Republic of China

    Fajie Li

  2. Dept. Computer Science, University of Auckland, P.O. Box 92019, Auckland, 1142, New Zealand

    Reinhard Klette

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  1. Fajie Li
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Correspondence to Fajie Li .

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Li, F., Klette, R. (2011). Watchman Routes. In: Euclidean Shortest Paths. Springer, London. https://doi.org/10.1007/978-1-4471-2256-2_11

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  • DOI: https://doi.org/10.1007/978-1-4471-2256-2_11

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