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Computing a shortest watchman path in a simple polygon in polynomial-time

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Algorithms and Data Structures (WADS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 955))

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Abstract

In this paper we present the first polynomial-time algorithm for finding the shortest polygonal chain in a simple polygon such that each point of the polygon is visible from some point on the chain. This chain is called the shortest watchman path, or equivalently, the shortest weakly visible curve of the polygon. In proving this result we also give polynomial time algorithms for finding the shortest aquarium-keeper's path that visits all edges of the polygon, and for finding the shortest postman path that visits all vertices of a polygon.

This paper has been supported by a grant from the Swedish Research Council for Engineering Sciences (Teknikvetenskapliga forskningsrådet).

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Authors and Affiliations

  1. Division of Computer Science, Luleå University of Technology, S-971 87, Luleå, Sweden

    Svante Carlsson & Håkan Jonsson

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  1. Svante Carlsson
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  2. Håkan Jonsson
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Editor information

Selim G. Akl Frank Dehne Jörg-Rüdiger Sack Nicola Santoro

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© 1995 Springer-Verlag Berlin Heidelberg

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Carlsson, S., Jonsson, H. (1995). Computing a shortest watchman path in a simple polygon in polynomial-time. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_56

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  • DOI: https://doi.org/10.1007/3-540-60220-8_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60220-0

  • Online ISBN: 978-3-540-44747-4

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