L_m distance

(definition)

Definition: The generalized distance between two points. In a plane with point p₁ at (x₁, y₁) and p₂ at (x₂, y₂), it is (|x₁ - x₂|^m + |y₁ - y₂|^m)^1/m.

Also known as Minkowski distance.

See also Euclidean distance, rectilinear, Manhattan distance, Hamming distance.

Note: This is easily generalized to higher dimensions. Euclidean distance is L₂ distance. Rectilinear, Manhattan or Hamming distance is L₁ distance. L_∞ distance is max(|x₁ - x₂|, |y₁ - y₂|). Adapted from [CLR90, page 912].

Author: PEB

More information

More formal definitions of distance measures. Wikipedia definition of distance in the mathematical or physical sense.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 11 February 2019.
HTML page formatted Wed Mar 13 12:42:46 2019.

Cite this as:
Paul E. Black, "L_m distance", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 11 February 2019. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/lmdistance.html