Constructing the R* Consensus Tree of Two Trees in Subcubic Time
The previously fastest algorithms for computing the R* consensus tree of two given (rooted) phylogenetic trees with a leaf label set of cardinalityn run in ?(n 3) time (Bryant and Berry in Adv. Appl. Math. 27(4):705732, 2001; Kannan et al. in SIAM J. Comput. 27(6):16951724, 1998). In this manuscript, we describe a new \(O(n^{2} \sqrt{\log n})\)-time algorithm to solve the problem. This is a significant improvement because the R* consensus tree is defined in terms of a set\(\mathcal {R}_{\mathit{maj}}\) which may contain ?(n 3) elements, so any direct approach that explicitly constructs \(\mathcal {R}_{\mathit{maj}}\) requires ?(n 3) time.
r* consensus tree phylogenetic tree triplet strong cluster apresjan cluster lowest common ancestor offline orthogonal range counting