Kannan, Balakrishnan; Manoj, Changat; Henry, Martyn Mulder; Ajitha, Subhamathi R(DMFA Slovenije, June 15, 2012)
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Abstract:
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 f+; g. 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
Kannan, Balakrishnan; Manoj, Changat; Henry, Martyn Mulder(Econometric Institute Research Papers, September 15, 2006)
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Abstract:
The Majority Strategy for finding medians of a set of clients on a graph
can be relaxed in the following way: if we are at v, then we move to a neighbor
w if there are at least as many clients closer to w than to v (thus ignoring the
clients at equal distance from v and w). The graphs on which this Plurality
Strategy always finds the set of all medians are precisely those for which the
set of medians induces always a connected subgraph
Description:
Report/Econometric Institute, Erasmus University Rotterdam