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Great-circle navigation or orthodromic navigation (related to orthodromic course; from Ancient Greek ορθός (orthós) 'right angle' and δρόμος (drómos) 'path') is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe.
Suppose you would like to find the shortest path between two intersections on a city map: a starting point and a destination. Dijkstra's algorithm initially marks the distance (from the starting point) to every other intersection on the map with infinity. This is done not to imply that there is an infinite distance, but to note that those ...
The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
Going the "long way round" on a great circle between two points on a sphere is a geodesic but not the shortest path between the points. The map t → t 2 {\displaystyle t\to t^{2}} from the unit interval on the real number line to itself gives the shortest path between 0 and 1, but is not a geodesic because the velocity of the corresponding ...
As an example, when searching for the shortest route on a map, h(x) might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points. For a grid map from a video game, using the Taxicab distance or the Chebyshev distance becomes better depending on the set of movements ...
Solution of a travelling salesperson problem: the black line shows the shortest possible loop that connects every red dot. The travelling salesman problem, also known as the travelling salesperson problem (TSP), asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns ...
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