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We consider a variant of the classical two median facility location problem on a tree in which vertices are allowed to have positive or negative weights. in trees with pos/neg-weights, Discrete Appl. Math. 105 (2000) 51–71). who looked at two objectives, finding the total minimum weighted distance (MWD) and the total weighted minimum distance (WMD). Their… (More)
We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is sparse. This answers a question of Hindman, Stepr¯ ans and Strauss.