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On Steiner's network problem
Published online by Cambridge University Press: 26 February 2010
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Let S be a point set of the Euclidean plane, such that
(i) S is bounded,
(ii) the closure of S has unit Lebesgue measure.
Let P be an arbitrary set of n points contained in S, and let l(P) denote the total length of the shortest system of lines connecting the points of P together. Define ln to be the supremum of l(P), taken over all sets P of n points in S. Beardwood, Halton, and Hammersley [1[ proved that there exists an absolute constant α, independent of S, such that
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