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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. In the maximum metric, the distance between two points is the maximum of the absolute values of differences of their x- and y ...
The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R. Likewise, the vertex, the point on the great circle with greatest latitude, is found by substituting σ = + 1 ⁄ 2 π. It may be convenient to parameterize the ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. 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 ...
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
Two primary problems of pathfinding are (1) to find a path between two nodes in a graph; and (2) the shortest path problem—to find the optimal shortest path. Basic algorithms such as breadth-first and depth-first search address the first problem by exhausting all possibilities; starting from the given node, they iterate over all potential ...
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.