A.R. Subhamathi (Ajitha)
http://repub.eur.nl/ppl/27914/
List of Publicationsenhttp://repub.eur.nl/eur_signature.png
http://repub.eur.nl/
RePub, Erasmus University RepositoryAxiomatic Characterization of the Median and
Antimedian Functions on Cocktail-Party Graphs and
Complete Graphs
http://repub.eur.nl/pub/77639/
Mon, 24 Nov 2014 00:00:01 GMT<div>M. Changat</div><div>D.S. Lekha</div><div>H.M. Mulder</div><div>A.R. Subhamathi</div>
__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 output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (or obnoxious) facility in a network.
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 an axiomatic characterization is obtained for the median and antimedian functions on complete graphs minus a perfect matching (also known as cocktail-party graphs). In addition a characterization of the antimedian function on complete graphs is presented.Consensus strategies for signed profiles on graphs
http://repub.eur.nl/pub/37740/
Fri, 15 Jun 2012 00:00:01 GMT<div>K. Balakrishnan</div><div>M. Changat</div><div>H.M. Mulder</div><div>A.R. Subhamathi</div>
The median problem is a classical problem in Location Theory: one searches for a
location that minimizes the average distance to the sites of the clients. This is for desired
facilities as a distribution center for a set of warehouses. More recently, for obnoxious
facilities, the antimedian was studied. Here one maximizes the average distance to the
clients. In this paper the mixed case is studied. Clients are represented by a profile, which
is a sequence of vertices with repetitions allowed. In a signed profile each element is
provided with a sign from <+,-> Thus one can take into account whether the client
prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all
median sets, or all antimedian sets, are connected are characterized. Various consensus
strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity.
Hypercubes are the only graphs on which Majority produces the median set for all signed
profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming
graphs, Johnson graphs and halfcubes.Consensus strategies for signed profiles on graphs
http://repub.eur.nl/pub/37742/
Fri, 15 Jun 2012 00:00:01 GMT<div>K. Balakrishnan</div><div>M. Changat</div><div>H.M. Mulder</div><div>A.R. Subhamathi</div>
The median problem is a classical problem in Location Theory: one searches for a
location that minimizes the average distance to the sites of the clients. This is for desired
facilities as a distribution center for a set of warehouses. More recently, for obnoxious
facilities, the antimedian was studied. Here one maximizes the average distance to the
clients. In this paper the mixed case is studied. Clients are represented by a profile, which
is a sequence of vertices with repetitions allowed. In a signed profile each element is
provided with a sign from (+,-). Thus one can take into account whether the client
prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all
median sets, or all antimedian sets, are connected are characterized. Various consensus
strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity.
Hypercubes are the only graphs on which Majority produces the median set for all signed
profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming
graphs, Johnson graphs and halfcubes.Consensus Strategies for Signed Profiles on Graphs
http://repub.eur.nl/pub/26664/
Mon, 17 Oct 2011 00:00:01 GMT<div>K. Balakrishnan</div><div>M. Changat</div><div>H.M. Mulder</div><div>A.R. Subhamathi</div>
The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes
http://repub.eur.nl/pub/22803/
Fri, 04 Mar 2011 00:00:01 GMT<div>K. Balakrishnan</div><div>M. Changat</div><div>H.M. Mulder</div><div>A.R. Subhamathi</div>
An antimedian of a profile $\\pi = (x_1, x_2, \\ldots , x_k)$ 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 the two classes of graphs on which the antimedian is
well-behaved: paths and hypercubes.