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In the Euclidean TSP (see below), the distance between two cities is the Euclidean distance between the corresponding points. In the rectilinear TSP, the distance between two cities is the sum of the absolute values of the differences of their x- and y-coordinates. This metric is often called the Manhattan distance or city-block metric.
Moreover, for each number of cities there is an assignment of distances between the cities for which the nearest neighbor heuristic produces the unique worst possible tour. (If the algorithm is applied on every vertex as the starting vertex, the best path found will be better than at least N/2-1 other tours, where N is the number of vertices.)
Greatest distance between any two points in the 50 states: 5,859 miles (9,429 km), from Kure Atoll, Hawaii, to Log Point, Elliott Key, Florida. Greatest distance between any two points in the contiguous 48 states: 2,901 miles (4,669 km), from North Farallon Island, California, to Sail Rock, east of West Quoddy Head, Maine.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude .
The longest continuous north–south distance on land is 7,590 km (4,720 mi) along the meridian 99°1'30"E, from the northern tip of Siberia in the Russian Federation ( 76°13′6″N 99°1′30″E. / 76.21833°N 99.02500°E / 76.21833; 99.02500. ), through Mongolia, China, and Myanmar, to a point on the south coast of Thailand ( 7°53 ...
The distance between two points in physical space is the length of a straight line between them, which is the shortest possible path. This is the usual meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two- and three-dimensional space.
The Strait of Gibraltar [1] is a narrow strait that connects the Atlantic Ocean to the Mediterranean Sea and separates Europe from Africa . The two continents are separated by 13 kilometres (8.1 miles; 7.0 nautical miles) of ocean at the Strait's narrowest point between Punta de Tarifa in Spain and Point Cires in Morocco. [2]
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle . It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the ...
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