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 29 September 2008.
HTML page formatted Mon Feb 2 13:10:39 2015.

Cite this as:
Paul E. Black, "L_m distance", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 29 September 2008. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/lmdistance.html