Localizing 2-medians on probabilistic and deterministic tree networks

Locating a single facility (the 1-median problem) on a deterministic tree network is very efficiently solved by Goldman's algorithm. This paper explores the possibility of efficiently solving the 2-median problem for both deterministic and probabilistic tree networks. Interesting properties (Theorems 1–4) are derived that relate the location of 1-median to the location of pairs of 2-medians. Two simple algorithms, the “Improved Link-Deletion” algorithm for the deterministic case and the “Selective Enumeration” algorithm for the probabilistic case, are presented which somewhat improve existing methods to determine 2-medians on tree networks.