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Encyclopedia > Museum guard problem

A visibility graph is a graph of intervisible locations. Each node or vertex in the graph represents a point location, and each edge represents a visible connection between them (that is, if two locations can see each other, an edge is drawn between them). In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ... Enhanced Data Rates for GSM Evolution (EDGE) is a digital mobile phone technology which acts as a bolt-on enhancement to 2G and 2. ...

Visibility graphs are classically regarded as two dimensional artefacts. They are drawn within a plan of a site, or in mathematical terms, a polygon. The polygon may or may not have holes (obstructions within the plan). Wiktionary has a definition of: Polygon A polygon (literally many angle, see Wiktionary for the etymology) is a closed planar path composed of a finite number of sequential line segments. ...

O'Rourke (1987) writes about various Art Gallery Theorems, where the plan is of a supposed art gallery. For the purposes of mathematics, an art gallery is simply an arbitrary polygon with or without holes, so they do not tend to look like plans of art galleries on the page; instead, they allow investigation into various art gallery problems. One art gallery problem considered by O'Rourke was raised by Klee in 1973. Klee asked: how many guards does it take to guard an art gallery?

The problem can be set for both polygons with or without holes.

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. A yagi antenna Most simply, an antenna is an electronic component designed to transmit or receive radio waves. ... Architecture (in Greek αρχή = first and τέχνη = craftsmanship) is the art and science of designing buildings and structures. ... Urban, city, or town planning, deals with design of the built environment from the municipal and metropolitan perspective. ... Autonomous robots are robots which can perform desired tasks in unstructured environments without continuous human guidance. ... A humanoid robot playing the trumpet In practical usage, a robot is a mechanical device which performs automated tasks, either according to direct human supervision, a pre-defined program or, a set of general guidelines, using artificial intelligence techniques. ... Ultrasound is sound with a frequency greater than the upper limit of human hearing, approximately 20 kilohertz. ... A sensor is a technological device or biological organ that detects, or senses, a signal or physical condition. ...

• O'Rourke, J. (1987). Art Gallery Theorems and Algorithms. Oxford University Press. ISBN 0195039653.

Results from FactBites:

 Visibility graph - Wikipedia, the free encyclopedia (219 words) 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.
 University of York | Dept of Physics | Colloquia (232 words) 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.
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