Stephan Friedrichs

Point guards and point clouds: solving general art gallery problems

In this video, we illustrate how one of the classical areas of computational geometry has gained in practical relevance, which in turn gives rise to new, fascinating geometric problems. In particular, we demonstrate how the robot platform IRMA3D can produce high-resolution, virtual 3D environments, based on a limited number of laser scans. Computing an optimal set of scans amounts to solving an instance of the Art Gallery Problem (AGP): Place a minimum number of stationary guards in a polygonal region P, such that all points in P are guarded.

The continuous 1.5D terrain guarding problem: Discretization, optimal solutions, and PTAS

In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP) we are given an

Engineering Art Galleries

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k-Stacks: High-density valet parking for automated vehicles

-monotone chain of line segments in

Facets for Art Gallery Problems

R^2

Energy-efficient voltage scheduling of peripheral components on wireless sensor nodes

(the terrain

Efficient reconfiguration of processing modules on FPGAs for space instruments

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A PTAS for the Continuous 1.5D Terrain Guarding Problem.

), and ask for the minimum number of guards (located anywhere on

Metastability-Containing Circuits

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Complexity of the General Chromatic Art Gallery Problem

) required to guard all of