Close-Neighbor-Interchange (CNI)

In any method, examining all possible topologiesRH_Topology is very time consuming.  This algorithm reduces the time spent searching by first producing a temporary tree, (e.g., an NJHC_Neighbor_Joining tree when an MEHC_Minimum_Evolution tree is being sought), and then examining all of the topologies that are different from this temporary tree by a topological distance The topological distance quantifies the extent of topological differences between two given trees. For unrooted, bifurcating trees, this distance is twice the number of interior branches at which the taxa are partitioned differently. of dT = 2 and 4.  If this is repeated many times, and all the topologies previously examined are avoided, one can usually obtain the tree being sought. 

For the MP method, the CNI search can start with a tree generated by the random addition of sequences.  This process can be repeated multiple times to find the MP tree.

See Nei & Kumar (2000)Nei_and_Kumar_2000 for details.