In phylogenetic analyses of molecular sequence data, partitioning involves estimating independent models of molecular evolution for different sets of sites in a sequence alignment. Choosing an appropriate partitioning scheme is an important step in most analyses because it can affect the accuracy of phylogenetic reconstruction. Despite this, partitioning schemes are often chosen without explici...

Given a tree T on n vertices, and k, b, s1, . . . , sb ∈ N, the Tree Partitioning problem asks if at most k edges can be removed from T so that the resulting components can be grouped into b groups such that the number of vertices in group i is si, for i = 1, . . . , b. The case when s1 = · · · = sb = n/b, referred to as the Balanced Tree Partitioning problem, was shown to be NP-complete for tr...