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Point Number Vector Dimension Graph Area Lattice In Mathbb Rn

1	Point
1	Vector
1	Dimension
1	Number
1	Graph
2	Area
3	Lattice In Mathbb Rn

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City Block Metric

The city-block metric, defined on $\mathbb{R}^n$ , is

$\displaystyle d(a,b) = \sum_{i=1}^n \vert b_i-a_i\vert$

where and are vectors in $\mathbb{R}^n$ with $a=(a_1,\ldots,a_n)$ and $b=(b_1,\ldots,b_n)$ .

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