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Good Illumination of Minimum Range

M. Abellanas,A. Bajuelos,Gregorio Hernández-Peñalver,F. Hurtado,I. Matos,Belén Palop

Published 2006 in arXiv.org

ABSTRACT

A point p is 1-well illuminated by a set F of n point lights if p lies in the interior of the convex hull of F. This concept corresponds to triangle-guarding or well-covering. In this paper we consider the illumination range of the light sources as a parameter to be optimized. First, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate a given point p. We also compute a minimal set of light sources that 1-well illuminates p with minimum illumination range. Second, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate all the points of a line segment with an O(n^2) algorithm. Finally, we give an O(n^2 log n) algorithm for preprocessing the data so that one can obtain the illumination range needed to 1-well illuminate a point of a line segment in O(log n) time. These results can be applied to solve problems of 1-well illuminating a trajectory by approaching it to a polygonal path.

PUBLICATION RECORD

  • Publication year

    2006

  • Venue

    arXiv.org

  • Publication date

    2006-06-02

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv cs/0606013
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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REFERENCES

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