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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.
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.
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.)
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 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 ...
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 .
A city is a human settlement of a notable size. The term "city" has different meanings around the world and in some places the settlement can be very small. Even where the term is limited to larger settlements, there is no universally agreed definition of the lower boundary for their size. [1] [2] In a more narrow sense, a city can be defined ...
Distance markers along the Rhine measure the distance from the bridge in the old city center of Konstanz. For most of its length, the Seerhein forms the border between Germany and Switzerland. The exception is the old city center of Konstanz, on the Swiss side of the river.
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