city-block metric

The city-block metric, defined on n, is


where a and b are vectors in n with a=(a1,,an) and b=(b1,,bn).

In two dimensionsMathworldPlanetmath and with discrete-valued vectors, when we can picture the set of points in × as a grid, this is simply the number of edges between points that must be traversed to get from a to b within the grid. This is the same problem as getting from corner a to b in a rectilinear downtown area, hence the name “city-block metric.”

Title city-block metric
Canonical name CityblockMetric
Date of creation 2013-03-22 12:12:57
Last modified on 2013-03-22 12:12:57
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 9
Author akrowne (2)
Entry type Definition
Classification msc 54E35
Synonym city-block distance
Synonym taxicab metric