论文信息 - On optimal embeddings of metrics in graphs

On optimal embeddings of metrics in graphs

Abstract This paper extends previous results of the authors. In particular, non-treerealizable metrics are investigated and it is shown that every finite metric has an optimal realization by a graph.

[1] J. M. S. S. Pereira,et al. A note on the tree realizability of a distance matrix , 1969 .

[2] S. Chaiken,et al. An Optimal Diagonal Tree Code , 1983 .

[3] A. K. Dewdney,et al. Diagonal Tree Codes , 1979, Inf. Control..

[4] P. Buneman. A Note on the Metric Properties of Trees , 1974 .

[5] É. Stotskii,et al. Optimal imbeddings of metrics in graphs , 1972 .

[6] Ye.A Smolenskii. A method for the linear recording of graphs , 1963 .

[7] Timothy J. Lowe,et al. Duality and Distance Constraints for the Nonlinear p-Center Problem and Covering Problem on a Tree Network , 1982, Oper. Res..

[8] Peter H. Sellers,et al. The Theory and Computation of Evolutionary Distances: Pattern Recognition , 1980, J. Algorithms.

[9] Manfred Eigen,et al. The origin of genetic information. , 1981, Scientific American.

[10] S. S. Yau,et al. Distance matrix of a graph and its realizability , 1965 .

[11] Wilfried Imrich,et al. Trees and Length Functions on Groups , 1983 .

[12] F. T. Boesch,et al. Properties of the distance matrix of a tree , 1969 .

[13] S. Hakimi,et al. The distance matrix of a graph and its tree realization , 1972 .

[14] Christina Zamfirescu,et al. Submatrices of non-tree-realizable distance matrices , 1982 .

[15] J. M. S. Simões-Pereira. A Note on Optimal and Suboptimal Digraph Realizations of Quasidistance Matrices , 1984 .