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.
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Entry modified 29 September 2008.
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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. 29 September 2008. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/lmdistance.html