Key points are not available for this paper at this time.
We consider the problem of fitting an n × n distance matrix D by a tree metric T. Let be the distance to the closest tree metric under the L_ norm; that is, =T\ T-D\. First we present an O (n2) algorithm for finding a tree metric T such that T-D 3. Second we show that it is NP-hard to find a tree metric T such that T-D < 98. This paper presents the first algorithm for this problem with a performance guarantee.
Agarwala et al. (Thu,) studied this question.