0 KB308 KB55 KB200820252013Balakrishnan, KannanChangat, ManojMulder, Henry MartynSubhamathi, Ajitha R.številka:1letnik:6str. 127-145COBISSID:16471129ISSN:1855-3966URN:URN:NBN:SI:doc-6YB6RQSNenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneahalfcubeHamming graphJohnson graphmajority rulemedianplurality strategyConsensus strategies for signed profiles on graphs|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 halfcubesTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije