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Topic: Museum guard problem

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  Visibility graph - Wikipedia, the free encyclopedia
A major open problem in this area is to characterize the visibility graphs of polygons.
In addition to theoretical problems, visibility graphs also have practical uses, for example, to calculate the placement of radio antennas, or as a tool used within architecture and urban planning through visibility graph analysis.
Visibility graphs are also used in mobile robotics as a (generally offline) path-planning tool when the geometry of the environment is known, although robots have been designed that collect isovist information as they explore the environment using ultrasound sensors, which can then be turned into a visibility graph of recognisable known locations.
en.wikipedia.org /wiki/Visibility_graph   (219 words)

 University of York | Dept of Physics | Colloquia
These are problems which are hard in the sense that no fast algorithms to solve them exist.
When studying problems on suitably parametrised ensembles, one finds phenomena strongly reminiscent of phase transitions.
One also observes phase regions, where the problem can be solved typically quickly using the available algorithms, i.e.
www.york.ac.uk /depts/phys/archive/colloquia/2005-06/colloquium-240506.htm   (232 words)

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