Guarding disjoint triangles and claws in the plane

Authors:
Csaba D. Tóth
Affiliations:
Institute for Theoretical Computer Science, ETH Zürich, CH-8092, Switzerland
Venue:
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Year:
2003

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Abstract

We consider the problem of guarding triangles in the plane and show that ⌊(5n+ 2)/4⌋ guards can monitor the boundaries and the free space of n disjoint triangles. This improves the best previously known upper bound ⌊4n/3⌋ + 1 due to Hoffmann, Kaufmann and Kriegel. We also consider the analogous problem for n disjoint claws in the plane and show that 3n/2 + O(1) guards are always sufficient and 3n/2 - O(1) are sometimes necessary.