The ℓ_p‐function on trees

Abstract A p ‐value of a sequence π = ( x 1 , x 2 ,…, x k ) of elements of a finite metric space ( X, d ) is an element x for which \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}$\sum_{i=1}^{k}d^p(x,x_i)$\end{document} is minimum. The function ℓ p with domain the set of all finite sequences defined by ℓ p (π) = { x : x is a p ‐value of π} is called the ℓ p ‐function on X . The ℓ p ‐functions with p = 1 and p = 2 are the well‐studied median and mean functions respectively. In this article, the ℓ p ‐function on finite trees is characterized axiomatically. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012