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].
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 Fri Feb 23 10:06:08 2018.
Cite this as:
Paul E. Black, "Lm distance", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 29 September 2008. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/lmdistance.html