the median function, which minimizes the sum of the distances to the client locations, three simple and natural axioms …, anonymity, betweenness, and consistency suffice on tree networks (continuous case) as shown by Vohra, and on cube-free median … graphs (discrete case) as shown by McMorris et.al.. In the latter paper, in the case of arbitrary median graphs, a fourth …

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average … client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all … Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed …

allowed. A median x of is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The … median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A … median graph is a graph for which every profile of length 3 has a unique median. Median graphs are well studied. They arise …

__Abstract__ A median (antimedian) of a profile of vertices on a graph $G$ is a vertex that minimizes (maximizes) the … remoteness value, that is, the sum of the distances to the elements in the profile. The median (or antimedian) function has as … obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by …