A p-value of a sequence π = (x1, x2,⋯, xk) of elements of a finite metric space (X, d) is an element x for which ∑i=1kdp(x,xi) is minimum. The function ℓpwith domain the set of all finite sequences defined by ℓp(π) = {x: x is a p-value of π} is called the ℓp-function on X. The ℓp-functions with p = 1 and p = 2 are the well-studied median and mean functions respectively. In this article, the ℓp-function on finite trees is characterized axiomatically.

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doi.org/10.1002/net.20463, hdl.handle.net/1765/34915
ERIM Article Series (EAS)
Erasmus Research Institute of Management

McMorris, F. R., Mulder, M., & Ortega, O. (2012). The ℓ
p-function on trees. Networks, 60(2), 94–102. doi:10.1002/net.20463