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Underlying graph and total length of optimal realizations of variable distance matrices

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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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Authors and Affiliations

  1. Hunter College and Graduate School, The City University of New York, 10021, New York, NY, USA

    J. M. S. Simões-Pereira

  2. Departamento de Matemática, Universidade de Coimbra, 3000, Coimbra, Portugal

    J. M. S. Simões-Pereira

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  1. J. M. S. Simões-Pereira
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Additional information

This work was supported by the National Science Foundation Grant DMS-8401686 and by the PSC/CUNY Research Award Program.

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Simões-Pereira, J.M.S. Underlying graph and total length of optimal realizations of variable distance matrices. Graphs and Combinatorics 3, 383–393 (1987). https://doi.org/10.1007/BF01788561

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  • DOI: https://doi.org/10.1007/BF01788561

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