Abstract
The general problem is to investigate, for acceptable values ofx, the optimal graph realization of a matrixD(x) obtained from a given tree-realizable distance matrixD as follows: we partition the index set ofD into two convex subsetsH andK, we subtractx from all entriesd hk andd kh whereh ? H andk ? K and we leave all other entries unchanged. We describe the optimal realization of the matrixD(x) and the behaviour of the total length of the optimal realization as a function ofx.
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