Establishing a Metric in Max-Plus Geometry
Uri Carl, Kevin W. O'Neill, Nicholas Ryder · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2012
Abstract. Using the characterization of the segments in the max-plus semimodule R n max, provided by Nitica and Singer in [5], we find a class of metrics on the finite part of R n max. 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. Acknowledgements: This paper was written during the summer 2012 mathematics