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Table 1 Basic facts for the closest metric problem

From: Ultrametric networks: a new tool for phylogenetic analysis

C D M L 1 L 2 L
Additive NP‐Hard+ NP‐Hard NP‐Hard*
Ultrametric NP‐Hard+ NP‐Hard P§
  1. +no approximation is known;
  2. *a 3‐approximation exists, due to Agarwal et al. [1];
  3. §due to Gower and Ross [3] (see also ([6], p.158), ([7], p.134), [2, 8]).