Abstract
let Q(x) denote the particle nearest any x EF R d with some fixed rule for breaking ties. We refer to any finite sequence of particles (q1, . . ., qK) with q1 = Q(x) and qK= Q(y) as a Q-path from x to y. Think of traveling from particle to particle as having a cost associated with it given by a penalty fiunction: a strictly increasing function f: RD-?_ R? with f(O) = 0. Letting I I denote Euclidean distance, T is defined by
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