Computing the nearest neighbor interchange metric for unlabeled binary trees is NP-complete

Abstract

Nearest neighbor interchange metric, Binary tree (dendogram), NP-completeness theory,

On computing the nearest neighbor interchange distance

“…Computing the nni distance between two unlabeled trees is also NPcomplete. This answers an open question in [3] for which an erroneous proof appeared in [23].…”

“…Computing the nni distance between two unlabeled trees is also NPcomplete. This answers an open question in [3] for which an erroneous proof appeared in [23].3. Biological applications motivate us to extend the nni distance to weighted phylogenies, where edge weights indicate the time-span of evolution along each edge.…”

“…The question is open even for the simpler case where the trees are unlabeled. The faulty NP-completeness proof [23] we mentioned above was for this case.…”

“…The complexity of computing the nni distance has been open for more than 25 years (since [29]). The problem is surprisingly subtle as witnessed by the history of many erroneous results, disproved conjectures and a faulty NP-completeness proof [2,19,20,23,22,26,34]. The question is open even for the simpler case where the trees are unlabeled.…”

“…distance, is thus an important issue in computational molecular biology. The nearest neighbor interchange (nni) distance [29,28,34, 3, 6,2,19,20,23,33,22,21,26] is a natural distance metric that has been extensively studied. Despite its many appealing aspects such as simplicity and sensitivity to tree topologies, computing this distance has remained very challenging, and many algorithmic and complexity issues about computing this distance have remained unresolved.…”