(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
Pictures and definitions of several distance measures. 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 E. Black.
Entry modified 31 May 2006.
HTML page formatted Mon Sep 11 09:46:04 2006.
Cite this as:
Paul E. Black, "Lm distance", in
Dictionary of Algorithms and Data
Structures [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 31 May 2006. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/lmdistance.html
