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Please use this identifier to cite or link to this item: http://purl.org/purl/4234

Title: Consensus strategies for signed profiles on graphs
Authors: Kannan, Balakrishnan
Manoj, Changat
Henry, Martyn Mulder
Ajitha, Subhamathi R
Keywords: Plurality strategy
majority rule
Hamming graph
Johnson graph
Math. Subj. Class.: 05C99, 05C12, 90B80
Issue Date: 15-Jun-2012
Publisher: DMFA Slovenije
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
Description: Ars Math. Contemp. 6 (2013) 127–145
URI: http://dyuthi.cusat.ac.in/purl/4234
ISSN: 1855-3966 (printed edn.), 1855-3974 (electronic edn.)
Appears in Collections:Dr. Kannan Balakrishnan

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