Definition

A metric (V,d)(V,d) is a tree metric if there exists a tree T=(V,ET)T = (V,E_T) with edge lengths such that d(u,v)=dT(u,v)d(u,v) = d_T(u,v).

References

  1. https://courses.grainger.illinois.edu/cs598csc/sp2009/lectures/lecture_23_draft.pdf
  2. Fakcharoenphol, Jittat, Satish Rao, and Kunal Talwar. "A tight bound on approximating arbitrary metrics by tree metrics." In Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, pp. 448-455. 2003. doi:10.1016/j.jcss.2004.04.011
  3. https://people.math.wisc.edu/~roch/evol-gen/roch-evolgen-notes6.pdf