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  • 1.
    Bose, Prosenjit
    et al.
    School of Computer Science, Carleton University, Ottawa, Ontario, Canada.
    Brodnik, Andrej
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science. IMFM, University of Ljubljana, Ljubljana, Slovenia.
    Carlsson, Svante
    University of Karlskona/Ronneby, Karlskona, Sweden.
    Demaine, Erik .D.
    Massachusetts Institute of Technology, Laboratory for Computer Science, Cambridge, MA, United States.
    Fleischer, Rudolf
    Department of Computer Science, Hong Kong University of Science and Technology, Kowloon, Hong Kong.
    López-Ortiz, Alejandro
    Department of Computer Science, University of Waterloo, Canada.
    Morin, Pat
    School of Computer Science, Carleton University, Ottawa, Ontario, Canada.
    Munro, J. Ian
    Department of Computer Science, University of Waterloo, Canada.
    Online routing in convex subdivisions2002In: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 12, no 4, p. 283-295Article in journal (Refereed)
    Abstract [en]

    We consider online routing algorithms for finding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4) there is no competitive online routing algorithm under the link distance metric even when the input graph is restricted to be a Delaunay, greedy, or minimum-weight triangulation.

  • 2.
    Carlsson, Svante
    et al.
    Luleå University of Technology.
    Nilsson, Bengt J.
    Department of Computer Science, Lund University.
    Ntafos, Simeon
    Computer Science Program, University of Texas at Dallas.
    Optimum guard covers and m-watchmen routes for restricted polygons1993In: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 3, no 1, p. 85-105Article in journal (Refereed)
    Abstract [en]

    A watchman, in the terminology of art galleries, is a mobile guard. We consider several watchman and guard problems for different classes of polygons. We introduce the notion of vision spans along a path (route) which provide a natural connection between the Art Gallery problem, the m-watchmen problem and the watchman route problem. We prove that finding the minimum number of vision points, i.e., static guards, along a shortest watchman route is NP-hard. We provide a linear time algorithm to compute the best set of static guards in a histogram polygon. The m-watchmen problem, minimize total length of routes for m watchmen, is NP-hard for simple polygons. We give a \Theta(n 3 + n 2 m 2 )-time algorithm to compute the best set of m watchmen in a histogram. 1 Introduction The problem of placing guards in an art gallery so that every point in the gallery is visible to at least one guard has been considered by several researchers. If the gallery is represented by a polygon, ...

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