Christoph Stamm

Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result

We study the problem of minimizing the number of guards positioned at a fixed height h such that each triangle on a given 2.5- dimensional triangulated terrain T is completely visible from at least one guard. We prove this problem to be NP-hard, and we show that it cannot be approximated by a polynomial time algorithm within a ratio of (1 - ∈) 1/35 ln n for any ∈ > 0, unless NP ⊆ TIME (nO(log log n)), where n is the number of triangles in the terrain. Since there exists an approximation algorithm that achieves an approximation ratio of ln n+1, our result is close to the optimum hardness result achievable for this problem.

A prototype system for light propagation in terrains

We present a prototype system for a simple version of electromagnetic wave propagation prediction in rural areas, using a real time exploration environment for very large topographic scenes. The wave propagation prediction algorithm is based on a simple line of sight approach, realized with a modified hidden surface removal algorithm. The system serves as a transmitter management tool for interactively placing transmitters and studying the effects. Improvements according to the propagation prediction and automatic optimized placement of transmitters are current subjects of our research.