Image processing and computer vision.
There are many distance transforms to measure the distance between two points.
Why is the Manhattan distance so called?
The taxicab geometry page on Wiki answers that :)
https://en.wikipedia.org/wiki/Taxicab_geometry
This is a good question.
Here is an application of the Manhattan distance that you may find interesting:
NADINE ABBOUD, MARTIN GRO¨ TSCHEL, THORSTEN KOCH, Mathematical Methods for Physical Layout of Printed Circuit Boards: An Overview, Konrad-Zuse-Zentrum
fur¨ Informationstechnik Berlin, 2006:
file:///Users/jfpeters/Downloads/ZR-06-29.pdf
See, for example, Section 3.2.1 Quadratic assignment, starting on page 4.
A nice introduction to the Manhattan distance is given in
Rolf Niedermeier, Peter Sandersy, On the Manhattan-Distance Between Points on Space-Filling Mesh-Indexing, 1996:
http://theinf1.informatik.uni-jena.de/publications/trsf.pdf
For the worst case scenario, see the attached image.
Manhattan distance is the simple sum of the horizontal and vertical components, whereas the diagonal distance might be computed by applying the Pythagorean theorem.
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