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Concerning the time bounds of existing shortest watchman route algorithms

  • Mikael Hammar
  • Bengt J. Nilsson
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1279)

Abstract

A watchman route in a polygon P is a route inside P such that each point in the interior of P is visible from at least one point along the route. The objective of the shortest watchman route problem is to minimize the length of the watchman route for a given polygon. In 1991 Chin and Ntafos claimed an O(n4) algorithm, solving the shortest watchman route problem for simple polygons, given a starting point of the route. Later, improvements of this result were presented by Tan, Hirata and Inagaki, decreasing the time-bound to O(n2). We prove that the time bound analyses of these algorithms are erroneous and that their true time bound is Ω(2n). Furthermore, a modification to the latest algorithm is given, restoring its time bound to O(n2).

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References

  1. 1.
    S. Carlsson, H. Jonsson, and B.J. Nilsson. Finding the shortest watchman route in a simple polygon. In Proc. 4th International Symposium on Algorithms and Computation, ISAAC'93, pages 58–67. Springer Verlag, Lecture Notes in Computer Science 762, 1993.Google Scholar
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    W. Chin and S. Ntafos. Optimum watchman routes. Information Processing Letters, 28:39–44, 1988.CrossRefGoogle Scholar
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    W. Chin and S. Ntafos. Shortest watchman routes in simple polygons. Discrete and Computational Geometry, 6(1):9–31, 1991.Google Scholar
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    X.-H. Tan and T. Hirata. Constructing shortest watchman routes by divide and conquer. In Proc. 4th International Symposium on Algorithms and Computation, pages 68–77. Springer Verlag, Lecture Notes in Computer Science 762, 1993.Google Scholar
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    X. H. Tan, T. Hirata, and Y. Inagaki. An incremental algorithm for constructing shortest watchman routes. In Proc. ISA '91 Algorithms, pages 163–175. Springer Verlag, Lecture Notes in Computer Science 557, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mikael Hammar
    • 1
  • Bengt J. Nilsson
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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