scholarly journals The t-median function on graphs

2006 ◽  
Vol 154 (18) ◽  
pp. 2599-2608 ◽  
Author(s):  
F.R. McMorris ◽  
Henry Martyn Mulder ◽  
Robert C. Powers
Keyword(s):  
Median Function

scholarly journals The median function on median graphs and semilattices

2000 ◽  
Vol 101 (1-3) ◽  
pp. 221-230 ◽  
Author(s):  
F.R. McMorris ◽  
H.M. Mulder ◽  
R.C. Powers
Keyword(s):  
Median Graphs ◽  
Median Function

scholarly journals AXIOMATIC CHARACTERIZATION OF THE ANTIMEDIAN FUNCTION ON PATHS AND HYPERCUBES

2012 ◽  
Vol 04 (04) ◽  
pp. 1250054 ◽  
Author(s):  
KANNAN BALAKRISHNAN ◽  
MANOJ CHANGAT ◽  
HENRY MARTYN MULDER ◽  
AJITHA R. SUBHAMATHI
Keyword(s):  
Axiomatic Characterization ◽  
Median Graphs ◽  
Obnoxious Facility ◽  
Location Function ◽  
Median Function

An antimedian of a profile π = (x1, x2, …, xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The 'converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for two classes of graphs on which the antimedian is well behaved: paths and hypercubes.

scholarly journals Robust estimation of the conditional median function at elliptical models

2001 ◽  
Vol 51 (4) ◽  
pp. 361-368 ◽  
Author(s):  
Christophe Croux ◽  
Catherine Dehon ◽  
Peter J. Rousseeuw ◽  
Stefan Van Aelst
Keyword(s):  
Robust Estimation ◽  
Conditional Median ◽  
Elliptical Models ◽  
Median Function

scholarly journals Five axioms for location functions on median graphs

2015 ◽  
Vol 07 (02) ◽  
pp. 1550013 ◽  
Author(s):  
F. R. McMorris ◽  
Henry Martyn Mulder ◽  
Beth Novick ◽  
R. C. Powers
Keyword(s):  
The Other ◽  
Axiomatic Characterizations ◽  
Median Graphs ◽  
Median Function

In previous work, two axiomatic characterizations were given for the median function on median graphs: one involving the three simple and natural axioms anonymity, betweenness and consistency; the other involving faithfulness, consistency and [Formula: see text]-Condorcet. To date, the independence of these axioms has not been a serious point of study. The aim of this paper is to provide the missing answers. The independent subsets of these five axioms are determined precisely and examples provided in each case on arbitrary median graphs. There are three cases that stand out. Here nontrivial examples and proofs are needed to give a full answer. Extensive use of the structure of median graphs is used throughout.

scholarly journals The median function on distributive semilattices

2003 ◽  
Vol 127 (2) ◽  
pp. 319-324 ◽  
Author(s):  
F.R McMorris ◽  
H.M Mulder ◽  
R.C Powers
Keyword(s):  
Median Function ◽  
Distributive Semilattices
Sign in / Sign up

Export Citation Format

Share Document