Using the characterization of the segments in the max-plus semimodule Rnmax, provided by Nitica and Singer, we find a class of metrics on the finite part of Rnmax. One of them is the Euclidean length of the max-plus segment connecting two points. This metric is not quasi-convex. There is exactly one other metric in our class that does possess this property. Each metric in our class is associated with a weighting function, which is concave and non-decreasing.
Prof. Viorel Nitica, Department of Mathematics, West Chester University
Carl, Uri; O'Neill, Kevin W.; and Ryder, Nicholas
"Establishing a Metric in Max-Plus Geometry,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 10.
Available at: http://scholar.rose-hulman.edu/rhumj/vol13/iss2/10