2011-06-06
An axiomatization of the median procedure on the n-cube
Publication
Publication
Discrete Applied Mathematics , Volume 159 - Issue 9 p. 939- 944
The general problem in location theory deals with functions that find sites to minimize some cost, or maximize some benefit, to a given set of clients. In the discrete case sites and clients are represented by vertices of a graph, in the continuous case by points of a network. The axiomatic approach seeks to uniquely distinguish certain specific location functions among all the arbitrary functions that address this problem by using a list of intuitively pleasing axioms. The median function minimizes the sum of the distances to the client locations. This function satisfies three simple and natural axioms: anonymity, betweenness, and consistency. They suffice on tree networks (continuous case) as shown by Vohra (1996) [19], and on cube-free median graphs (discrete case) as shown by McMorris et al. (1998) [9]. In the latter paper, in the case of arbitrary median graphs, a fourth axiom was added to characterize the median function. In this note we show that the above three natural axioms still suffice for the hypercubes, a special instance of arbitrary median graphs.
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doi.org/10.1016/j.dam.2011.02.001, hdl.handle.net/1765/25515 | |
Discrete Applied Mathematics | |
Organisation | Erasmus School of Economics |
Mulder, M., & Novick, B. (2011). An axiomatization of the median procedure on the n-cube. Discrete Applied Mathematics, 159(9), 939–944. doi:10.1016/j.dam.2011.02.001 |