5-th Phylogenetic Root Construction for Strictly Chordal Graphs

Reconstruction of an evolutionary history for a set of organisms is an important research subject in computational biology. One approach motivated by graph theory constructs a relationship graph based on pairwise evolutionary closeness. The approach builds a tree representation equivalent to this graph such that leaves of the tree, corresponding to the organisms, are within a specified distance of k in the tree if connected in the relationship graph. This problem, the kth phylogenetic root construction, has known linear time algorithms for k ≤ 4. However, the computational complexity is unknown if k ≥ 5. We present a polynomial time algorithm for strictly chordal relationship graphs if k = 5.