Planar point location using persistent search trees
Communications of the ACM
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Illumination of polygons with vertex lights
Information Processing Letters
Planar separators and parallel polygon triangulation
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Handbook of discrete and computational geometry
Dynamic fine-grained localization in Ad-Hoc networks of sensors
Proceedings of the 7th annual international conference on Mobile computing and networking
Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks
IEEE Transactions on Computers
Range-free localization schemes for large scale sensor networks
Proceedings of the 9th annual international conference on Mobile computing and networking
Computational geometry column 48
ACM SIGACT News
Guarding curvilinear art galleries with edge or mobile guards
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Improved Bounds for Wireless Localization
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Guarding curvilinear art galleries with vertex or point guards
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Coverage with k-transmitters in the presence of obstacles
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Coverage with k-transmitters in the presence of obstacles
Journal of Combinatorial Optimization
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We consider the problem of placing a small number of angle guards inside a simple polygon P so asto provide efficient proofs that any given point is inside P. Each angle guard views an infinite wedge of the plane, and a point can prove membership in P if it is inside the wedges for a set of guards whose common intersection contains no points outside the polygon. This model leads to a broad class of new art gallery type problems, which we call "sculpture garden" problems and for which we provide upper and lower bounds. In particular, we show there is a polygon P such that a "natural" angle-guard vertex placement cannot fully distinguish between pointson the inside and outside of P (even if we place a guard at every vertex of P), which implies that Steiner-point guards are sometimes necessary. More generally, we show that, for any polygon P, there is a set of n+2(h-1) angle guards that solve the sculpture garden problem for P, where h is the number of holes in P (so a simple polygon can be defined with n-2 guards). In addition, we show that, for any orthogonal polygon P, the sculpture garden problem can besolved using n/2 angle guards. We also give an example of a class of simple (non-general-position) polygons that have sculpture garden solutions using O(√n) guards, and we show this bound is optimal to within a constant factor. Finally, while optimizing the number of guards solving a sculpture garden problem for a particular P is of unknown complexity, we show how to find in polynomial time a guard placement whose size is within a factor of 2 of the optimal number for any particular polygon.